Title data
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.
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Project financing: 
Andere European Union "FP7PeopleITN" programme 
Abstract
In this paper, we present a numerical algorithm for computing ISS Lyapunov functions for continuoustime systems which are inputtostate 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 righthand side our algorithm is in principle able to deliver an ISS Lyapunov function. For $C^2$ righthand sides a more efficient algorithm is proposed.
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 Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 11 Feb 2015 12:00) [Currently Displayed]