Publications

Below you find a list of my publications sorted in chronological order. For my editorial work, please have a look at my short cv. For the abstract of each publications click on the title. In addition, you can use the following links for

publications in 2014

A. Boccia, L. Grüne, K. Worthmann: Stability and feasibility of state-constrained linear MPC without stabilizing terminal constraints
in: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), 2014, 8 pages, to appear
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T. Damm, L. Grüne, M. Stieler, K. Worthmann: An exponential turnpike theorem for dissipative discrete time optimal control problems
SIAM Journal on Control and Optimization, 23 pages, 2014, to appear
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A. Fleig, L. Grüne, R. Guglielmi: Some results on Model Predictive Control for the Fokker-Planck equation
Extended Abstract
in: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), 2014, 3 pages, to appear
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L. Grüne: Nominal Model Predictive Control
in: Encyclopedia of Systems and Control, Tariq Samad, John Baillieul (eds.)
2014, Article No. 364751
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L. Grüne: Numerical methods for nonlinear optimal control problems
in: Encyclopedia of Systems and Control, Tariq Samad, John Baillieul (eds.)
2014, Article No. 364958
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L. Grüne, F. Allgöwer, R. Findeisen, J. Fischer, D. Groß, U. D. Hanebeck, B. Kern, M. A. Müller, J. Pannek, M. Reble, O. Stursberg, P. Varutti, K. Worthmann: Distributed and Networked Model Predictive Control
in: Control Theory of Digitally Networked Dynamic Systems, Chapter 4, J. Lunze (ed.)
Springer Verlag, 2014, 111 - 167
DOI: 10.1007/978-3-319-01131-8_4


L. Grüne, S. Hirche, O. Junge, P. Koltai, D. Lehmann, J. Lunze, A. Molin, R. Sailer, M. Sigurani, C. Stöcker, F. Wirth: Event-Based Control
in: Control Theory of Digitally Networked Dynamic Systems, Chapter 5, J. Lunze (ed.)
Springer Verlag, 2014, 169 - 261
DOI: 10.1007/978-3-319-01131-8_5


L. Grüne, C.M. Kellett: Strong implication-form ISS-Lyapunov functions for discontinuous discrete-time systems
in: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), 2014, 8 pages, to appear
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L. Grüne, V.G. Palma: On the benefit of re-optimization in optimal control under perturbations
in: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), 2014, 8 pages, to appear
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L. Grüne, M. Sigurani: A Lyapunov based nonlinear small-gain theorem for discontinuous discrete-time large-scale systems
in: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), 2014, 8 pages, to appear
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L. Grüne, M. Sigurani: Construction of event-based ISS controllers on coarse quantizations
Preprint, University of Bayreuth, 2013, 6 pages
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L. Grüne, M. Stieler: Asymptotic stability and transient optimality of economic MPC without terminal constraints
Preprint, University of Bayreuth, 2014, 26 pages
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L. Grüne, M. Stieler: A Lyapunov function for economic MPC without terminal conditions
Preprint, University of Bayreuth, 2014, 6 pages
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L. Grüne, M. Zanon: Periodic optimal control, dissipativity and MPC
Extended Abstract
in: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), 2014, 4 pages, to appear
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L. Grüne, H. Zidani: Zubov's equation for state-constrained perturbed nonlinear systems
Mathematical Control and Related Fields - MCRF, 19 pages, 2014, to appear
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H. Li, R. Baier, L. Grüne, S.F. Hafstein, F. Wirth: Computation of local ISS Lyapunov functions via linear programming
in: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), 2014, 7 pages, to appear
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J. Lunze, L. Grüne: Introduction to Networked Control Systems
in: Control Theory of Digitally Networked Dynamic Systems, Chapter 1, J. Lunze (ed.)
Springer Verlag, 2014, 1 - 30
DOI: 10.1007/978-3-319-01131-8_1


K. Worthmann, C.M. Kellett, P. Braun, L. Grüne, S.R. Weller: Distributed and decentralized control of residential energy systems incorporating battery storage
Preprint, University of Bayreuth, 2014, 8 pages
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K. Worthmann, C.M. Kellett, L. Grüne, S.R. Weller: Distributed control of residential energy systems using a Market Maker
in: Proceedings of the IFAC World Congress, Cape Town, South Africa, 2014, 6 pages, to appear
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K. Worthmann, M. Reble, L. Grüne, F. Allgöwer: The role of sampling for stability and performance in unconstrained nonlinear model predictive control
SIAM Journal on Control and Optimization 52 (1), 581–605, 2014
DOI: 10.1137/12086652X
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publications in 2013

N. Altmüller, L. Grüne: A comparative stability analysis of Neumann and Dirichlet boundary MPC for the heat equation
in: Proceedings of the 1st IFAC Workshop on Control of Systems Modeled by Partial Differential Equations - CPDE 2013, 2013, 161 - 166, Paper #48
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A. Boccia, L. Grüne, K. Worthmann: Stability and feasibility of state constrained MPC without stabilizing terminal constraints
Preprint, University of Bayreuth, 2013, 23 pages
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L. Grüne: Economic receding horizon control without terminal constraints
Automatica, 49, 725 - 734, 2013
DOI: 10.1016/j.automatica.2012.12.003
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L. Grüne, I. Karafyllis: Lyapunov function based step size control for numerical ODE solvers with application to optimization algorithms
in: Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his 60th Birthday, K. Hüper and J. Trumpf (ed.)
CreateSpace, 2013, 183 - 210
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L. Grüne, C.M. Kellett: ISS-Lyapunov functions for discontinuous discrete-time systems
Preprint, University of Bayreuth, 2013, 24 pages
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L. Grüne, W. Semmler, M. Stieler: Using nonlinear model predictive control for dynamic decision problems in economics
Preprint, University of Bayreuth, 2013, 27 pages
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L. Grüne, M. Sigurani: Numerical ISS controller design via a dynamic game approach
in: Proceedings of the 52nd IEEE Conference on Decision and Control - CDC 2013, 2013, 1732 - 1737
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M. Sigurani, C. Stöcker, L. Grüne, J. Lunze : Experimental evaluation of two complementary decentralized event-based control methods
Preprint, University of Bayreuth, 2013, 49 pages
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publications in 2012

N. Altmüller, L. Grüne: Distributed and boundary model predictive control for the heat equation
GAMM Mitteilungen 35 (2), 131 - 145, 2012
DOI: 10.1002/gamm.201210010
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R. Baier, L. Grüne, S.F. Hafstein: Linear programming based Lyapunov function computation for differential inclusions
Discrete and Continuous Dynamical Systems- Series B 17 (1), 33 - 56, 2012
DOI: 10.3934/dcdsb.2012.17.33
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A. Greiner, L. Grüne, W. Semmler: Economic growth and the transition from non-renewable to renewable energy
Environment and Development Economics, 33 pages, 2012 (date of preprint), 2014 (expected publication date), to appear
DOI: 10.1017/S1355770X13000491
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L. Grüne: Economic MPC and the role of exponential turnpike properties
in: Oberwolfach Reports, 2012, 678-681
DOI: 10.4171/OWR/2012/12
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L. Grüne: Economic MPC without terminal constraints
Extended Abstract
in: Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012), 2012, CD-ROM, Paper No. 58, 4 pages
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L. Grüne: NMPC without terminal constraints
in: Proceedings of the IFAC Conference on Nonlinear Model Predictive Control 2012 (NMPC'12), 2012, 1 - 13
DOI: 10.3182/20120823-5-NL-3013.00030
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L. Grüne, T. Jahn: Computing reachable sets via barrier methods on SIMD architectures
in: Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), J. Eberhardsteiner, H.J. Böhm, F.G. Rammerstorfer (eds.)
Vienna University of Technology, Vienna, Austria, 2012, CD-ROM, Paper No. 1518, 20 pages
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L. Grüne, J. Pannek, M. Seehafer, K. Worthmann: Analysis of Unconstrained Nonlinear MPC Schemes with Time Varying Control Horizon
in: Proceedings of the 51st IEEE Conference on Decision and Control, Maui, Hawaii, 2012, 2605 - 2610
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L. Grüne, J. Pannek, K. Worthmann: Ensuring Stability in Networked Systems with Nonlinear MPC for Continuous Time Systems
in: Proceedings of the 51st IEEE Conference on Decision and Control, Maui, Hawaii, 2012, 14 - 19
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L. Grüne, K. Worthmann: A distributed NMPC scheme without stabilizing terminal constraints
in: Distributed Decision Making and Control, Chapter 12, R. Johansson, A. Rantzer (eds.)
Springer Verlag, 2012, 259 - 285
DOI: 10.1007/978-1-4471-2265-4_12
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M. Hänel, S. Kuhn, D. Henrich, L. Grüne, J. Pannek: Optimal camera placement to measure distances conservatively regarding static and dynamic obstacles
Int. J. Sensor Networks 12 (1), 25 - 36, 2012
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V. Palma, L. Grüne: Stability, performance and robustness of sensitivity-based multistep feedback NMPC
Extended Abstract
in: Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012), 2012, CD-ROM, Paper No. 68, 4 pages
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publications in 2011

H. Aoyama, L. Grüne, W. Semmler, Y. Fujiwara, W. Souma: Fluctuation of firm size in the long-run and bimodal distribution
Advances in Operations Research 2011, 21 pages, 2011, Article ID 269239
DOI: 10.1155/2011/269239
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R. Findeisen, L. Grüne, J. Pannek, P. Varutti: Robustness of prediction based delay compensation for nonlinear systems
in: Proceedings of the 18th IFAC World Congress, Milano, Italy, 2011, 203 - 208
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L. Grüne: Optimal invariance via receding horizon control
in: Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, Florida, USA, 2011, 2668 - 2673
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L. Grüne, J. Pannek: Nonlinear Model Predictive Control: Theory and Algorithms
in: xii + 370 pages, Communications and Control Engineering, Springer Verlag, 2011, xii + 370 pages
DOI: 10.1007/978-0-85729-501-9


L. Grüne, O.S.Serea: Differential games and Zubov's method
SIAM Journal on Control and Optimization 49 (6), 2349 - 2377, 2011
DOI: 10.1137/100787829
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I. Karafyllis, L. Grüne: Feedback stabilization methods for the numerical solution of systems of ordinary differential equations
Discrete and Continuous Dynamical Systems - Series B 16 (1), 283 - 317, 2011
DOI: 10.3934/dcdsb.2011.16.283
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publications in 2010

N. Altmüller, L. Grüne, K. Worthmann: Instantaneous control of the linear wave equation
in: Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2010), Budapest, Hungary, 2010, 1895 - 1899
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N. Altmüller, L. Grüne, K. Worthmann: Performance of NMPC schemes without stabilizing terminal constraints
in: Recent Advances in Optimization and its Applications in Engineering, M. Diehl, F. Glineur, E. Jarlebring, W. Michiels (eds.)
Springer Verlag, 2010, 289 - 298
DOI: 10.1007/978-3-642-12598-0_25
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N. Altmüller, L. Grüne, K. Worthmann: Receding Horizon optimal control for the wave equation
in: Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, Georgia, 2010, 3427 - 3432
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R. Baier, L. Grüne, S.F. Hafstein: Computing Lyapunov functions for strongly asymptotically stable differential inclusions
in: Proceedings of NOLCOS 2010, Bologna, Italy, 2010, 1098 - 1103
DOI: 10.3182/20100901-3-IT-2016.00132
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L. Grüne: Worst case vs. average performance estimates for unconstrained NMPC schemes
in: Proceedings of the GAMM Annual Meeting, Karlsruhe, Germany, 2010, 607 - 608
DOI: 10.1002/pamm.201010296
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A. Greiner, L. Grüne,W. Semmler: Growth and climate change: threshold and multiple equilibria
in: Dynamic Systems, Economic Growth, and the Environment, J. Crespo Cuaresma, T. P. Palokangas, A. Tarasyev (eds.)
Springer Verlag, 2010, 63 - 79
DOI: 10.1007/978-3-642-02132-9_4
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L. Grüne, S. Jerg, O. Junge, D. Lehmann, J. Lunze, F. Müller, M. Post: Two complementary approaches to event-based control
at-Automatisierungstechnik 58 (Special Issue on Networked Control Systems), 173 - 182, 2010
DOI: 10.1524/auto.2010.0832
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L. Grüne, F. Müller: Global optimal control of quantized systems
in: Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2010), Budapest, Hungary, 2010, 1231 - 1237
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L. Grüne, J. Pannek: Analysis of unconstrained NMPC schemes with incomplete optimization
in: Proceedings of NOLCOS 2010, Bologna, Italy, 2010, 238 - 243
DOI: 10.3182/20100901-3-IT-2016.00124
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L. Grüne, J. Pannek, M. Seehafer, K. Worthmann: Analysis of unconstrained nonlinear MPC schemes with varying control horizon
SIAM Journal on Control and Optimization 48 (8), 4938 - 4962, 2010
DOI: 10.1137/090758696
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L. Grüne, S. Sager, F. Allgöwer, H. G. Bock, M. Diehl: Predictive planning and systematic action - on the control of technical processes
in: Production Factor Mathematics, M.Grötschel, K. Lucas, V. Mehrmann (eds.)
Springer Verlag, 2010, 9 - 37
DOI: 10.1007/978-3-642-11248-5_2
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L. Grüne, M. von Lossow, J. Pannek, K. Worthmann: MPC: implications of a growth condition on exponentially controllable systems
in: Proceedings of NOLCOS 2010, Bologna, Italy, 2010, 385 - 390
DOI: 10.3182/20100901-3-IT-2016.00225
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L. Grüne, M. von Lossow, K. Worthmann: NMPC suboptimality estimates for sampled-data continuous systems
in: Recent Advances in Optimization and its Applications in Engineering, M. Diehl, F. Glineur, E. Jarlebring, W. Michiels (eds.)
Springer Verlag, 2010, 329 - 338
DOI: 10.1007/978-3-642-12598-0_29
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publications in 2009

F. Camilli, L. Grüne, F. Wirth: Domains of attraction of interconnected systems: A Zubov method approach
in: Proceedings of the European Control Conference (ECC) 2009, Budapest, Hungary, 2009, 91 - 96
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L. Grüne: Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems
SIAM Journal on Control and Optimization 48, 1206 - 1228, 2009
DOI: 10.1137/070707853
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L. Grüne, O. Junge: Gewöhnliche Differentialgleichungen - Eine Einführung aus der Perspektive der Dynamischen Systeme
Vieweg + Teubner Verlag, 2009,


L. Grüne, O. Junge: Set oriented construction of globally optimal controllers
at-Automatisierungstechnik 57, 287 - 295, 2009
DOI: 10.1524/auto.2009.0777
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L. Grüne, I. Karafyllis: Feedback stabilization methods for the numerical solution of systems of ordinary differential equations
in: Proceedings of the International Conference on Numerical Analysis ans Applied Mathematics ICNAAM 2009, AIP Conference Proceedings 1168, Rethymno, Crete, Greece, 2009, 152 - 155
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L. Grüne, F. Müller: An algorithm for event-based optimal feedback control
in: Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, 2009, 5311 - 5316
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L. Grüne, D. Nesic, K. Worthmann: Digital redesign of nonlinear multi-input systems
in: Oberwolfach Reports 11, 2009, 619 - 622
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L. Grüne, J. Pannek: Practical NMPC suboptimality estimates along trajectories
Systems & Control Letters 58, 161 - 168, 2009
DOI: 10.1016/j.sysconle.2008.10.012
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L. Grüne, J. Pannek, K. Worthmann: A networked unconstrained nonlinear MPC scheme
in: Proceedings of the European Control Conference (ECC) 2009, Budapest, Hungary, 2009, 371 - 376
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L. Grüne, J. Pannek, K. Worthmann: A prediction based control scheme for networked systems with delays and packet dropouts
in: Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, 2009, 537 - 542
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L. Grüne, S. Sager, F. Allgöwer, H. G. Bock, M. Diehl: Vorausschauend planen, gezielt handeln - über die Regelung und Steuerung technischer Prozesse
in: Produktionsfaktor Mathematik, M. Grötschel, K. Lucas, V. Mehrmann (eds.)
Springer Verlag, 2009, 27 - 62
DOI: 10.1007/978-3-540-89435-3
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L. Grüne, W. Semmler, C. Öhrlein: Dynamic consumption and portfolio decisions with time varying asset returns
The Journal of Wealth Management 12 (2), 21 - 47, 2009
DOI: 10.3905/JWM.2009.12.2.021


publications in 2008

L. Grüne: Input-to-state stability, numerical dynamics and sampled-data control
GAMM-Mitteilungen 31, 94 - 114, 2008
DOI: 10.1002/gamm.200890005
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L. Grüne: Optimization based stabilization of nonlinear control systems
in: Proceedings of the Large-Scale Scientific Computations (LSSC07) in Sozopol, Bulgaria, I. Lirkov, S. Margenov, J. Wasniewski (eds.)
Lecture Notes in Computer Science 4818, Springer Verlag, 2008, 52 - 65
DOI: 10.1007/978-3-540-78827-0_5
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L. Grüne, F. Camilli, F. Wirth: Control Lyapunov Functions and Zubov's Method
SIAM Journal on Control and Optimization 47, 301 - 326, 2008
DOI: 10.1137/06065129X
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L. Grüne, O. Junge: Global optimal control of perturbed systems
Journal of Optimization Theory and Applications (JOTA) 136, 411 - 429, 2008
DOI: 10.1007/s10957-007-9312-z
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L. Grüne, F. Müller: Set oriented optimal control using past information
in: Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), CD-Rom, Paper 125.pdf, 6 pages, Blacksburg, Virginia, 2008,
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L. Grüne, D. Nesic, J. Pannek, K. Worthmann: Redesign techniques for nonlinear sampled-data systems
at-Automatisierungstechnik 56 (Special Issue on Digitally Networked Systems), 38 - 48, 2008
DOI: 10.1524/auto.2008.0684
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L. Grüne, J. Pannek: Trajectory based suboptimality estimates for receding horizon controllers
in: Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), CD-Rom, Paper 023.pdf, 6 pages, Blacksburg, Virginia, 2008,
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L. Grüne, A. Rantzer: On the infinite horizon performance of receding horizon controllers
IEEE Transactions on Automatic Control 53, 2100 - 2111, 2008
DOI: 10.1109/TAC.2008.927799
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L. Grüne, W. Semmler: Asset Pricing with Loss Aversion
Journal of Economic Dynamics and Control 32, 3253 - 3274, 2008
DOI: 10.1016/j.jedc.2008.01.002
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L. Grüne, K. Worthmann: Nonlinear sampled-data redesign: analytical formulas and their practical implementation
in: Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), CD-Rom, Paper 084.pdf, 6 pages, Blacksburg, Virginia, 2008,
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L. Grüne, K. Worthmann: Sampled-data redesign for nonlinear multi-input systems
in: Geometric Control and Nonsmooth Analysis, F. Ancona, A. Bressan, P. Cannarsa, F. Clarke, P. R. Wolenski (eds.)
World Scientific, Singapore, 2008, 206 - 227
DOI: 10.1142/9789812776075_0011
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L. Grüne, K. Worthmann, D. Nesic: Continuous-time controller redesign for digital implementation: a trajectory based approach
Automatica 44, 225 - 232, 2008
DOI: 10.1016/j.automatica.2007.05.003
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publications in 2007

S. Becker,L. Grüne, W. Semmler: Comparing Accuracy of Second Order Approximation and Dynamic Programming
Computational Economics 30, 65 - 91, 2007
DOI: 10.1007/s10614-007-9087-1
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L. Grüne: Computing minimal optimization horizons for stabilizing unconstrained MPC schemes
in: Proceedings of the 6th International Congress on Industrial and Applied Mathematics (ICIAM 07) and GAMM Annual Meeting, Zürich, Switzerland, 2007, 4130007 - 4130008
DOI: 10.1002/pamm.200700203
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L. Grüne: Computing stability and performance bounds for unconstrained NMPC schemes
in: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, Louisiana, 2007, 93 - 1268
DOI: 10.1109/CDC.2007.4434156
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L. Grüne, O. Junge: Approximately optimal nonlinear stabilization with preservation of the Lyapunov function property
in: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, Louisiana, 2007, 702 - 707
DOI: 10.1109/CDC.2007.4434428
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L. Grüne, O. Junge: An efficient algorithm for perturbed shortest path problems
in: Proceedings of the 6th International Congress on Industrial and Applied Mathematics (ICIAM 07) and GAMM Annual Meeting, Zürich, Switzerland, 2007, 1025003 - 1025004
DOI: 10.1002/pamm.200700714
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L. Grüne, P.E. Kloeden, S. Siegmund, F. Wirth: Lyapunov's second method for nonautonomous differential equations
Discrete and Continuous Dynamical Systems - Series A 18 (Special Issue on Nonautonomous, Stochastic and Hamiltonian Dynamical Systems), 375 - 403, 2007
DOI: 10.3934/dcds.2007.18.375
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L. Grüne, D. Nesic, J. Pannek: Model predictive control for nonlinear sampled-data systems
in: Assessment and Future Directions of Nonlinear Model Predictive Control (NMPC05), F. Allgöwer, L. Biegler, R. Findeisen (eds.)
Lecture Notes in Control and Information Sciences 358, Springer Verlag, Heidelberg, 2007, 105 - 113
DOI: 10.1007/978-3-540-72699-9
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L. Grüne, W. Semmler: Asset Pricing with Dynamic Programming
Computational Economics 29, 233 - 265, 2007
DOI: 10.1007/s10614-006-9063-1
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L. Grüne, W. Semmler, L. Bernard: Firm value, diversified capital assets, and credit risk: towards a theory of default correlation
Journal of Credit Risk 3, 81 - 109, 2007/08
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publications in 2006

L. Grüne, F. Bauer, W. Semmler: Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations
Applied Numerical Mathematics 56, 1196 - 1210, 2006
DOI: 10.1016/j.apnum.2006.03.011
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L. Grüne, F. Camilli, A. Cesaroni, F. Wirth: Stabilization of controlled diffusions via Zubov's method
Stochastics & Dynamics 6, 373 - 394, 2006
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L. Grüne, O. Junge: Optimal stabilization of hybrid systems using a set oriented approach
in: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), Kyoto, Japan, 2006, 2089 - 2093
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L. Grüne, P. E. Kloeden: Higher order numerical approximation of switching systems
Systems & Control Letters 55, 746 - 754, 2006
DOI: 10.1016/j.sysconle.2006.03.002
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L. Grüne, D. Nesic: A receding horizon control approach to sampled-data implementation of continuous-time controllers
Systems & Control Letters 55, 660 - 672, 2006
DOI: 10.1016/j.sysconle.2005.09.013
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L. Grüne, D. Nesic, K. Worthmann: High order approximations by sampled-data feedback
in: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), Kyoto, Japan, 2006, 1780 - 1787
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L. Grüne, A. Ratzer: Suboptimality estimates for receding horizon controllers
in: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), Kyoto, Japan, 2006, 120 - 127
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L. Grüne, P. Saint-Pierre: An invariance kernel representation of ISDS Lyapunov functions
Systems & Control Letters 55, 736 - 745, 2006
DOI: 10.1016/j.sysconle.2006.02.003
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publications in 2005

F. Camilli, L. Grüne, F. Wirth: Calculating the domain of attraction: Zubov's method and extensions
in: Proceedings of the Stability and Control Processes Conference (SCP 2005), dedicated to the 75th birthday anniversary of V. I. Zubov, Saint Petersburg, Russia, 2005, 27 - 36
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F. Camilli, L. Grüne, F. Wirth: Zubov's method for stochastic control systems
in: Proceedings of the 16th IFAC World Congress, DVD-ROM, Paper No. Mo-M20-TO/4, Prague, Czech Republic, 2005,
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L. Grüne, O. Junge: A set oriented approach to optimal feedback stabilization
Systems & Control Letters 54, 169 - 180, 2005
DOI: 10.1016/j.sysconle.2004.08.005
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L. Grüne, O. Junge: Constructing robust feedback laws by set oriented numerical methods
in: Proceedings of the GAMM Annual Meeting, Luxembourg, 2005, 157 - 162
DOI: 10.1002/pamm.200510059
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L. Grüne, M. Kato, W. Semmler: Solving ecological management problems using dynamic programming
Journal of Economic Behavior & Organization 57, 448 - 473, 2005
DOI: 10.1016/j.jebo.2005.04.002
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L. Grüne, D. Nesic: Lyapunov based continuous-time nonlinear controller redesign for sampled-data implementation
Automatica 41, 1143 - 1156, 2005
DOI: 10.1016/j.automatica.2005.03.001
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L. Grüne, D. Nesic: Nonlinear sampled-data controller redesign via Lyapunov functions
in: Proceedings of the 16th IFAC World Congress, DVD-ROM, Paper No. Fr-A17-TO/5, Prague, Czech Republic, 2005,
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L. Grüne, D. Nesic, J. Pannek: Model predictive sampled-data redesign for nonlinear systems
in: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (ECC2005), Sevilla, Spain, 2005, 36 - 41
DOI: 10.1109/CDC.2005.1582127
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L. Grüne, D. Nesic, J. Pannek: Redesign techniques for nonlinear sampled-data control
in: Oberwolfach Reports 11, 2005, 584 - 586
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L. Grüne, P. Saint-Pierre: A set valued characterization of ISDS Lyapunov functions
in: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (ECC2005), Sevilla, Spain, 2005, 4718 - 4723
DOI: 10.1109/CDC.2005.1582907
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L. Grüne, W. Semmler: Default risk, asset pricing and debt control
Journal of Financial Econometrics 3, 79 - 106, 2005
DOI: 10.1093/jjfinec/nbi006
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L. Grüne, W. Semmler, M. Sieveking: Creditworthyness and thresholds in a credit market model with multiple equilibria
Economic Theory 25, 287 - 315, 2005
DOI: 10.1007/s00199-003-0442-8
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publications in 2004

F. Camilli, L. Grüne, F. Wirth: Characterizing controllability probabilities of stochastic control systems via Zubov's method
in: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS2004), CD-ROM, WA3, Paper No. 65, Leuven, Belgium, 2004,
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F. Camilli, L. Grüne, F. Wirth: Construction of Lyapunov functions on the domain of asymptotic nullcontrollability: numerics
in: Proceedings of NOLCOS 2004, Stuttgart, Germany, 2004, 883 - 888
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F. Camilli, L. Grüne, F. Wirth: Construction of Lyapunov functions on the domain of asymptotic nullcontrollability: theory
in: Proceedings of NOLCOS 2004, Stuttgart, Germany, 2004, 877 - 882
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L. Grüne: Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation
Numerische Mathematik 99, 85 - 112, 2004
DOI: 10.1007/s00211-004-0555-4
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L. Grüne: Quantitative aspects of the input-to-state stability property
in: Optimal Control, Stabilization, and Nonsmooth Analysis (MCT03), M. de Queiroz, M. Malisoff, P.Wolenski (eds.)
Lecture Notes in Control and Information Sciences 301, Springer Verlag, Heidelberg, 2004, 215 - 230
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L. Grüne: Robust asymptotic controllability under time-varying perturbations
Stochastics & Dynamics 4, 297 - 316, 2004
DOI: 10.1142/S0219493704001085
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L. Grüne, W. Semmler: Using dynamic programming with adaptive grid scheme for optimal control problems in economics
Journal of Economic Dynamics and Control 28 (12), 2427 - 2456, 2004
DOI: 10.1016/j.jedc.2003.11.002
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publications in 2003

L. Grüne: Attraction rates, robustness and discretization of attractors
SIAM Journal on Numerical Analysis 41, 2096 - 2113, 2003
DOI: 10.1137/S003614290139411X
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L. Grüne, F. Camili: Characterizing attraction probabilities via the stochastic Zubov equation
Discrete and Continuous Dynamical Systems - Series B 3, 457 - 468, 2003
DOI: 10.3934/dcdsb.2003.3.457
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L. Grüne, P. E. Kloeden: Numerical schemes of higher order for a class of nonlinear control systems
in: Numerical Methods and Applications, I. Dimov, I. Lirkov, S. Margenov, Z. Zlatev (eds.)
Springer Lecture Notes in Computer Science 2542, Borovets, Bulgaria, 2003, 213 - 220
DOI: 10.1007/3-540-36487-0
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L. Grüne, D. Nesic: Optimization based stabilization of sampled-data nonlinear systems via their approximate discrete-time models
SIAM Journal on Control and Optimization 42, 98 - 122, 2003
DOI: 10.1137/S036301290240258X
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publications in 2002

F. Camilli, L. Grüne, F. Wirth: A generalization of Zubov's method to perturbed systems
in: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, 2002, 3518 - 3523
DOI: 10.1109/CDC.2002.1184420
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F. Colonius, L. Grüne (eds.)
:
Dynamics, Bifurcations and Control (NCN)
in: xi + 303 pages, Lecture Notes in Control and Information Sciences 273, Springer Verlag, 2002, xi + 303 pages
DOI: 10.1007/3-540-45606-6
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S. Cyganowski, L. Grüne, P. E. Kloeden: MAPLE for Jump-Diffusion Stochastic Differential Equations in Finance
in: Programming Languages and Systems in Computational Economics and Finance, S.S. Nielsen (ed.)
Kluwer Academic Publishers, Dordrecht, 2002, 441 - 460
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L. Grüne: Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization
in: Lecture Notes in Mathematics 1783, Springer Verlag, 2002,
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L. Grüne: Gain preserving Lyapunov functions for perturbed and controlled systems
in: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, 2002, 707 - 712
DOI: 10.1109/CDC.2002.1184587
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L. Grüne: Input-to-state dynamical stability and its Lyapunov function characterization
IEEE Transactions on Automatic Control 47, 1499 - 1504, 2002
DOI: 10.1109/TAC.2002.802761
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L. Grüne: Quantitative aspects of the input-to-state stability property
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS2002), CD-Rom, Article TUA4-4, South Bend, Indiana, 2002,
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L. Grüne, D. Nesic: Stabilization of sampled-data nonlinear systems via their approximate models: an optimization based approach
in: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, 2002, 1934 - 1939
DOI: 10.1109/CDC.2002.1184810
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publications in 2001

S. Cyganowski, L. Grüne, P. E. Kloeden: MAPLE for Stochastic Differential Equations
in: Theory and Numerics of Differential Equations, J.F. Blowey, J.P. Coleman, A.W. Craig (eds.)
Springer Verlag, 2001, 127 - 178
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L. Grüne: Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations
in: Numerical Methods for Viscosity Solutions and Applications, M. Falcone, Ch. Makridakis (eds.)
World Scientific, Singapore, 2001, 153 - 172
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L. Grüne: Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization
Habilitation thesis, J.W. Goethe-Universität Frankfurt, 2001


L. Grüne: Persistence of attractors for one-step discretizations of ordinary differential equations
IMA Journal of Numerical Analysis 21, 751 - 767, 2001
DOI: 10.1093/imanum/21.3.751
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L. Grüne: Subdivision techniques for the computation of domains of attraction and reachable sets
in: Proceedings of NOLCOS 2001, St. Petersburg, Russia, 2001, 762 - 767
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L. Grüne, F. Camilli, F. Wirth: A generalization of Zubov's method to perturbed systems
SIAM Journal on Control and Optimization 40, 496 - 515, 2001
DOI: 10.1137/S036301299936316X
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L. Grüne, P. E. Kloeden: Discretization, inflation and perturbation of attractors
in: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems (DANSE), B. Fiedler (ed.)
Springer Verlag, 2001, 399 - 416
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L. Grüne, P. E. Kloeden: Higher order numerical schemes for affinely controlled nonlinear systems
Numerische Mathematik 89, 669 - 690, 2001
DOI: 10.1007/s002110000279
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L. Grüne, P. E. Kloeden: Pathwise Approximation of Random Ordinary Differential Equations
BIT - Numerical Mathematics 41, 710 - 721, 2001
DOI: 10.1023/A:1021995918864
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publications in 2000

F. Camilli, L. Grüne, F. Wirth: A regularization of Zubov's equation for robust domains of attraction
in: Nonlinear Control in the Year 2000 Volume 1 (NCN), A. Isidori, F. Lamnabhi-Lagarrigue, W. Respondek (eds.)
Lecture Notes in Control and Information Sciences 258, Springer Verlag, London, 2000, 277 - 290
DOI: 10.1007/BFb0110202
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M. Falcone, L. Grüne, F. Wirth: A maximum time approach to the computation of robust domains of attraction
in: EQUADIFF 99, Berlin, B. Fiedler, K. Gröger, J. Sprekels (eds.)
World Scientific, Singapore, 2000, 844 - 849
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L. Grüne: A uniform exponential spectrum for linear flows on vector bundles
Journal of Dynamics and Differential Equations 12, 435 - 448, 2000
DOI: 10.1023/A:1009024610394
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L. Grüne: Attractors under perturbation and discretization
in: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, 2118 - 2122
DOI: 10.1109/CDC.2000.914107
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L. Grüne: Computation of the Lyapunov Spectrum
in: F. Colonius, W. Kliemann, The Dynamics of Control, Appendix D, Birkhäuser, 2000, 569 - 596


L. Grüne: Convergence Rates of Perturbed Attracting Sets with Vanishing Perturbations
Journal of Mathematical Analysis and Applications 244, 369 - 392, 2000
DOI: 10.1006/jmaa.2000.6707
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L. Grüne: Homogeneous state feedback stabilization of homogeneous systems
in: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, 3409 - 3414
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L. Grüne: Homogeneous state feedback stabilization of homogeneous systems
SIAM Journal on Control and Optimization 38, 1288 - 1214, 2000
DOI: 10.1137/S0363012998349303
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L. Grüne, F. Camilli: Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis 38, 1540 - 1560, 2000
DOI: 10.1137/S003614299834798X
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L. Grüne, F. Camilli, F. Wirth: Homogeneous control Lyapunov functions for homogeneous control systems
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS2000), CD-Rom, Article B99, Perpignan, 2000,
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L. Grüne, F. Camilli, F. Wirth: Zubov's method for perturbed differential equations
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS2000), CD-Rom, Article B100, Perpignan, 2000,
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L. Grüne, E. Sontag, F. Wirth: On equivalence of exponential and asymptotic stability under changes of variables
in: EQUADIFF 99, Berlin, B. Fiedler, K. Gröger, J. Sprekels (eds.)
World Scientific, Singapore, 2000, 850 - 852
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L. Grüne, F. Wirth: Computing control Lyapunov functions via a Zubov type algorithm
in: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, 2129 - 2134
DOI: 10.1109/CDC.2000.914109
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L. Grüne, F . Wirth: On the rate of convergence of infinite horizon discounted optimal value functions
Nonlinear Analysis: Real World Applications 1, 499 - 515, 2000
DOI: 10.1016/S0362-546X(99)00288-6
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publications in 1999

L. Grüne: Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations
Systems & Control Letters 38, 27 - 35, 1999
DOI: 10.1016/S0167-6911(99)00044-4
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L. Grüne: Stabilization by sampled and discrete feedback with positive sampling rate
in: Stability and Stabilization of Nonlinear Systems (NCN), Chapter 9, D. Aeyels, F. Lamnabhi-Lagarrigue, A. van der Schaft (eds.)
Lecture Notes in Control and Information Sciences 246, Springer Verlag, London, 1999, 165 - 182
DOI: 10.1007/1-84628-577-1
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L. Grüne, M . Metscher, M. Ohlberger: On Numerical Algorithm and Interactive Visualization for Optimal Control Problems
Computing and Visualization in Science 1 (4), 221 - 229, 1999
DOI: 10.1007/s007910050020
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L. Grüne, E. Sontag, F. Wirth: Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes
Systems & Control Letters 38, 127 - 134, 1999
DOI: 10.1016/S0167-6911(99)00053-5
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L. Grüne, E. Sontag, F. Wirth: On the equivalence between asymptotic and exponential stability, and between ISS and finite H-infinity gain
in: Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, Arizona, 1999, 1220 - 1225
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L. Grüne, F. Wirth: Feedback stabilization of discrete-time homogeneous semi-linear systems
Systems & Control Letters 37, 19 - 30, 1999
DOI: 10.1016/S0167-6911(98)00110-8
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publications in 1998

F. Camilli, L. Grüne: Maximal solutions for a class of singular Hamilton-Jacobi equations
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS98), Padova, 1998, 447 - 450
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L. Grüne, F. Wirth: On linear convergence of discounted optimal control problems with vanishing discount rate
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS98), Padova, 1998, 185 - 188
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L. Grüne: Asymptotic Controllability and Exponential Stabilization of Nonlinear Control Systems at Singular Points
SIAM Journal on Control and Optimization 36, 1585 - 1603, 1998
DOI: 10.1137/S0363012997315919
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L. Grüne: Numerical stabilization at singular points
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS98), Padova, 1998, 633 - 636
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L. Grüne: On input-to-state stabilizability of semilinear control systems
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS98), Padova, 1998, 181 - 184
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L. Grüne: On the relation between discounted and average optimal control problems
Journal of Differential Equations 148, 65 - 99, 1998
DOI: 10.1006/jdeq.1998.3451
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L. Grüne, F. Wirth: Stabilization of discrete-time bilinear systems
in: Proceedings of the GAMM Jahrestagung 1997, ZAMM, Supplement 3, Regensburg, 1998, 925 - 926
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publications in 1997

L. Grüne: A Spectral Condition for Asymptotic Controllability and Stabilization at Singular Points
in: Proceedings of the 36th IEEE Conference on Decision and Control in San Diego, US, California, 1997, 4431 - 4435
DOI: 10.1109/CDC.1997.649648
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L. Grüne: An Adaptive Grid Scheme for the discrete Hamilton-Jacobi-Bellman Equation
Numerische Mathematik 75, 319 - 337, 1997
DOI: 10.1007/s002110050241
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L. Grüne: Discrete Feedback Stabilization of Nonlinear Control Systems at a Singular Point
in: Proceedings of the European Control Conference (ECC) 1997, CD-Rom, Paper No. 806, Brussels, 1997,
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publications in 1996

L. Grüne: Discrete Feedback Stabilization of Semilinear Control Systems
ESAIM: Control, Optimisation and Calculus of Variations 1, 207 - 224, 1996
DOI: 10.1051/cocv:1996106
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L. Grüne: Numerical Stabilization of Bilinear Control Systems
SIAM Journal on Control and Optimization 34, 2024 - 2050, 1996
DOI: 10.1137/S0363012994272290
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L. Grüne: Numerische Berechnung des Lyapunov-Spektrums bilinearer Kontrollsysteme
in: ausgezeichnet mit dem Universitätspreis der Universität Augsburg, PhD thesis, Logos-Verlag, Berlin-University of Augsburg, 1996
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publications in 1994

L. Grüne: Numerische optimale Steuerung und Stabilisierung
Diploma thesis, University of Augsburg, 1994
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University of Bayreuth -