Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian: Computation of local ISS Lyapunov functions with low gains via linear programming.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2015
. - 19 S.

Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)

264735-SADCO

Project financing:

Andere
European Union "FP7-People-ITN" programme

Abstract

In this paper, we present a numerical algorithm for computing ISS Lyapunov functions for continuous-time systems which are 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. The objective of the linear programming problem is to minimize the gain. We show that for every ISS system with a locally Lipschitz right-hand side our algorithm is in principle able to deliver an ISS Lyapunov function. For $C^2$ right-hand sides a more efficient algorithm is proposed.

Further data

Item Type:

Preprint, postprint

Additional notes (visible to public):

Contents:
1. Introduction,
2. Notations and Preliminaries,
3. The algorithm,
3.1 Definitions,
3.2 Interpolation errors,
3.3 The Algorithm,
4. Main results
5. Examples,
6. Conclusions,
7. Acknowledgement.

Keywords:

nonlinear systems; local input-to-state stability; local ISS Lyapunov function; robust Lyapunov function; linear programming