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Computation of Local ISS Lyapunov Functions Via Linear Programming

Abstract : In this paper, we present a numerical algorithm for computing a local ISS Lyapunov function for systems which are locally input-to-state stable (ISS) on compact subsets of the state space. The algorithm relies on a linear programming problem and computes a continuous, piecewise affine ISS Lyapunov function on a simplicial grid covering the given compact set excluding a small neighborhood of the origin. We show that the ISS Lyapunov function delivered by the algorithm is a viscosity subsolution of a partial differential equation. Index Terms--Nonlinear systems, Local input-to-state stability, Local ISS Lyapunov function, Linear programming, Viscosity subsolution
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https://hal.inria.fr/hal-01068706
Contributor : Estelle Bouzat <>
Submitted on : Friday, September 26, 2014 - 10:53:08 AM
Last modification on : Friday, August 23, 2019 - 3:08:02 PM
Long-term archiving on: : Saturday, December 27, 2014 - 10:46:00 AM

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Huijuan Li, Robert Baier, Lars Grüne, Sigurđur Freyr Hafstein, Fabian Wirth. Computation of Local ISS Lyapunov Functions Via Linear Programming. MTNS 2014, 2014, Groningen, Netherlands. ⟨hal-01068706⟩

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