Computation of continuous and piecewise affine Lyapunov functions for discrete-time systems

Title: Computation of continuous and piecewise affine Lyapunov functions for discrete-time systems
Creator: Li, Huijuan; Hafstein, Sigurður; Kellett, Christopher M.
Relation: ARC.FT110100746 http://purl.org/au-research/grants/arc/FT110100746
Relation: Journal of Difference Equations and Applications Vol. 21, Issue 6, p. 486-511
Publisher Link: http://dx.doi.org/10.1080/10236198.2015.1025069
Publisher: Taylor & Francis
Resource Type: journal article
Date: 2015
Description: In this paper, we present a new approach for computing Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. Given a suitable triangulation of a compact neighbourhood of the origin, a continuous and piecewise affine function can be parameterized by the values at the vertices of the triangulation. If these vertex values satisfy system-dependent linear inequalities, the parameterized function is a Lyapunov function for the system. We propose calculating these vertex values using constructions from two classical converse Lyapunov theorems originally due to Yoshizawa and Massera. Numerical examples are presented to illustrate the proposed approach.
Subject: Lyapunov theory; nonlinear systems; converse theorems; computational methods
Identifier: http://hdl.handle.net/1959.13/1339075
Identifier: uon:28171
Identifier: ISSN:1023-6198
Language: eng
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