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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