Computation of Local ISS Lyapunov Functions for Discrete-time Systems Via Linear Programming

Titelangaben

Li, Huijuan ; Grüne, Lars:
Computation of Local ISS Lyapunov Functions for Discrete-time Systems Via Linear Programming.
In: Journal of Mathematical Analysis and Applications. Bd. 438 (März 2016) Heft 2 . - S. 701-719.
ISSN 0022-247X
DOI: https://doi.org/10.1016/j.jmaa.2016.01.045

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Abstract

This paper presents a numerical algorithm for computing ISS Lyapunov functions for discrete-time systems which are input-to-state stable (ISS) on compact subsets of the state space. The algorithm relies on solving a linear optimization problem and delivers a continuous and piecewise affine ISS Lyapunov function on a suitable triangulation covering the given compact set excluding a small neighbourhood of the origin. The objective of the linear optimization problem is to minimize the ISS gain. It is shown that for every ISS system there exist a suitable triangulation such that the proposed algorithm terminates successfully.