# 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

- Citations and bibliometrics for my publications from Google Scholar
- Reviews of my publications in Zentralblatt MATH
- Reviews of my publications in MathSciNet
- Reviews I have written for Zentralblatt MATH

(for some of these links you need access rights for the respective databases)

## 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

Download as PDF

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

Download as PDF

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:
*
*

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L. Grüne, M. Sigurani:
**A Lyapunov based nonlinear small-gain theorem for discontinuous discrete-time large-scale systems**

in:
*
*

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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:
*
*

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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:
*
*

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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

Download as PDF (external link)

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

Download as PDF (external link)

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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

Download as PDF (external link)

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

Download as PDF (external link)

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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

Download as PDF (external link)

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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

Download as PDF
(File "gruene_pannek_worthmann_ecc_2009.pdf")

Download as PDF
(File "gruene_pannek_worthmann_ecc_2009_extended.pdf")

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,

Download as PDF

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,

Download as PDF

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,

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

## 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,

Download as PDF

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

Download as PDF

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

Download as PDF

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,

Download as PDF

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

Download as PDF

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

Download as PDF

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,

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

## 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

Download as PDF

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

Download as PDF

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

Download as PDF

## 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

Download as PDF

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

Download as PDF

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,

Download as PDF

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

Download as PDF

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

Download as PDF

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,

Download as PDF

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

Download as PDF

## 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

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

L. Grüne, P. E. Kloeden:
**Higher order numerical schemes for affinely controlled nonlinear systems**

*Numerische Mathematik*
**89**,
669 - 690,
2001

DOI:
10.1007/s002110000279

Download as PDF

L. Grüne, P. E. Kloeden:
**Pathwise Approximation of Random Ordinary Differential Equations**

*BIT - Numerical Mathematics*
**41**,
710 - 721,
2001

DOI:
10.1023/A:1021995918864

Download as PDF

## 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

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

L. Grüne:
**Homogeneous state feedback stabilization of homogeneous systems**

*SIAM Journal on Control and Optimization*
**38**,
1288 - 1214,
2000

DOI:
10.1137/S0363012998349303

Download as PDF

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

Download as PDF

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,

Download as PDF

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,

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

## 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

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

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

Download as PDF

## 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

Download as PDF

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

Download as PDF

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

Download as PDF

L. Grüne:
**Numerical stabilization at singular points**

in:
*Proceedings of the Mathematical Theory of Networks and Systems (MTNS98),*
*
*
Padova,
1998,
633 - 636

Download as PDF

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

Download as PDF

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

Download as PDF

L. Grüne, F. Wirth:
**Stabilization of discrete-time bilinear systems**

in:
*Proceedings of the GAMM Jahrestagung 1997,*
*
*
*ZAMM, Supplement*
**3**,
Regensburg,
1998,
925 - 926

Download as PDF

## 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

Download as PDF

L. Grüne:
**An Adaptive Grid Scheme for the discrete Hamilton-Jacobi-Bellman Equation**

*Numerische Mathematik*
**75**,
319 - 337,
1997

DOI:
10.1007/s002110050241

Download as PDF

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,

Download as PDF

## 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

Download as PDF

L. Grüne:
**Numerical Stabilization of Bilinear Control Systems**

*SIAM Journal on Control and Optimization*
**34**,
2024 - 2050,
1996

DOI:
10.1137/S0363012994272290

Download as PDF

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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