"Input-to-State Stability"
Mini course
Institute for Systems Theory in Engineering
Universität Stuttgart, November 23 and 30, 2004
Prof. Dr. Lars Grüne, Universität Bayreuth
Place and time: please see the course page at the Universität Stuttgart for this information
Summary: This mini course gives an introduction to the input-to-state stability (ISS) property, providing an overview about techniques for working with ISS and some of its applications.
| Lectures | |
| I. | Introduction and basic definitions, November 23 (mainly based on [5] but using also material from the other references) |
| Slides (PDF format) | |
| II. | Relation to other stability concepts, November 23 (first part based on [3,2], second part on H-infinity based on [4]) |
| Slides (PDF format) | |
| III. | Lyapunov functions and quantitative aspects, November 30 (first part based on [2], second part on [6], see also [9] for a more survey-like paper on quantitative aspects) |
| Slides (PDF format) | |
| IV. | Applications and ISS controller design, November 30 (small gain theorem based on [1,6], discretization on [10], controller design on [8,7]) |
| Slides (PDF format) | |
| References | |
| [0] | Eduardo D. Sontag, Smooth stabilization implies coprime factorization, IEEE Transactions on Automatic Control, 34(1989): 435-443. |
| Preprint version (PDF format, from E.D. Sontag's web page) | |
| [1] | Zhong-Ping Jiang, Andrew R. Teel, and Laurent Praly, Small gain theorem for ISS systems and applications, Mathematics of Control, Signals and Systems 7 (1994): 95-120. |
| [2] | Eduardo D. Sontag, Yuan Wang, On characterizations of the input-to-state stability property, Systems and Control Letters 24(1995): 351-359. |
| Preprint version (PDF format, from E.D. Sontag's web page) | |
| [3] | Eduardo D. Sontag, Yuan Wang, New characterizations of input to state stability, IEEE Transactions on Automatic Control 41(1996): 1283-1294. |
| Preprint version (PDF format, from E.D. Sontag's web page) | |
| [4] | Lars Grüne, Eduardo D. Sontag and Fabian R. Wirth, Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes, Systems and Control Letters, 38 (1999): 127-134. |
| Preprint version (PDF format, from E.D. Sontag's web page) | |
| [5] | Eduardo D. Sontag, The ISS philosophy as a unifying framework for stability-like behavior, in Nonlinear Control in the Year 2000, Volume 2, A. Isidori, F. Lamnabhi-Lagarrigue, and W. Respondek, eds., Lecture Notes in Control and Information Sciences vol. 259, Springer-Verlag, Berlin, 2000, 443-468. |
| Preprint version (PDF format, from E.D. Sontag's web page) | |
| [6] | Lars Grüne, Input-to-state dynamical stability and its Lyapunov function characterization, IEEE Transactions on Automatic Control, 47(2002): 1499-1504. |
| Preprint version (PDF format, from my web page) | |
| [7] | Daniel Liberzon, Eduardo D. Sontag, and Yuan Wang, Universal construction of feedback laws achieving ISS and integral-ISS disturbance attenuation , Systems and Control Letters 46(2002): 111-127. |
| Preprint version, Erratum (PDF format, from E.D. Sontag's web page) | |
| [8] | Michael Malisoff, Ludovic Rifford, and Eduardo D. Sontag, Asymptotic controllability implies input to state stabilization, SIAM J. Control and Optimization, 42(2004): 2221-2238. |
| Preprint version (PDF format, from E.D. Sontag's web page) | |
| [9] | Lars Grüne, Quantitative aspects of the input-to-state stability property, in Optimal Control, Stabilization, and Nonsmooth Analysis (MCT03), M. de Queiroz, M. Malisoff, and P. Wolenski, eds., Lecture Notes in Control and Information Sciences vol. 301, Springer-Verlag, Heidelberg, 2004, 215-230. |
| Preprint version (PDF format, from my web page) | |
| [10] | Lars Grüne, Attraction rates, robustness and discretization of attractors, SIAM J. Numerical Analysis, 41(2003), 2096-2113 |
| Preprint version (PDF format, from my web page) | |