Linear programming based Lyapunov function computation for differential inclusions

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
MR Nummer: 2843270
Zentralblattnummer: 1235.93222
Mathematics Subject Classification Code: 93D30 93D20 (34D20 34A60 34A36)
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Abstract:

We present a numerical algorithm for computing Lyapunov functions for a class of strongly asymptotically stable nonlinear differential inclusions which includes spatially switched systems and systems with uncertain parameters. The method relies on techniques from nonsmooth analysis and linear programming and constructs a piecewise affine Lyapunov function. We provide necessary background material from nonsmooth analysis and a thorough analysis of the method which in particular shows that whenever a Lyapunov function exists then the algorithm is in principle able to compute it. Two numerical examples illustrate our method.

Contents:

1. Introduction
2. Notation and preliminaries
3. Lyapunov functions
4. The algorithm
5. Examples

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