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Linear programming based Lyapunov function computation for differential inclusions. (English) Zbl 1235.93222
Summary: 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.

MSC:
93D30 Lyapunov and storage functions
93D20 Asymptotic stability in control theory
34D20 Stability of solutions to ordinary differential equations
34A60 Ordinary differential inclusions
34A36 Discontinuous ordinary differential equations
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