Computing Lyapunov functions for strongly asymptotically stable differential inclusions

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

Smart-Link: http://www.nolcos2010.unibo.it/
DOI: 10.3182/20100901-3-IT-2016.00132
Keywords: Lyapunov functions; stability of nonlinear systems; strongly asymptotical stability;differential inclusions; switched systems; piecewise linear hybrid systems; linear programming; numerical methods; nonsmooth analysis
Mathematics Subject Classification Code: 93D30 (93D20 34A36 34A60 90C05 34A38 37B25)
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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 switched systems and systems with uncertain parameters. The method relies on techniques from nonsmooth analysis and linear programming and leads to a piecewise affine Lyapunov function. We provide a thorough analysis of the method and present two numerical examples.

Contents:

1. Introduction
2. Notation and Preliminaries
3. Lyapunov Functions
4. The Algorithm
5. Examples

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