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.
In: Discrete and Continuous Dynamical Systems. Series B.
Vol. 20
(2015)
Issue 8
.
 pp. 24772495.
ISSN 15313492
DOI: https://doi.org/10.3934/dcdsb.2015.20.2477
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Project financing: 
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union 
Abstract in another language
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 14 Feb 2015 22:00)
 Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 08 Oct 2015 10:44) [Currently Displayed]