Linear programming based Lyapunov function computation for differential inclusions

Titelangaben

Baier, Robert ; Grüne, Lars ; Freyr Hafstein, Sigurđur:
Linear programming based Lyapunov function computation for differential inclusions.
In: Discrete and Continuous Dynamical Systems. Series B. Bd. 17 (2012) Heft 1 . - S. 33-56.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2012.17.33

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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.