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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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. 2014, Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. 〈hal-01068706〉

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