Computing continuous and piecewise affine lyapunov functions for nonlinear systems

Title: Computing continuous and piecewise affine lyapunov functions for nonlinear systems
Creator: Hafstein, Sigurdur F.; Kellett, Christopher M.; Li, Huijuan
Relation: Journal of Computational Dynamics Vol. 2, Issue 2, p. 227-246
Publisher Link: http://dx.doi.org/10.3934/jcd.2015004
Publisher: American Institute of Mathematical Sciences (AIMS)
Resource Type: journal article
Date: 2016
Description: We present a numerical technique for the computation of a Lyapunov function for nonlinear systems with an asymptotically stable equilibrium point. The proposed approach constructs a partition of the state space, called a triangulation, and then computes values at the vertices of the triangulation using a Lyapunov function from a classical converse Lyapunov theorem due to Yoshizawa. A simple interpolation of the vertex values then yields a Continuous and Piecewise Affine (CPA) function. Verification that the obtained CPA function is a Lyapunov function is shown to be equivalent to verification of several simple inequalities. Numerical examples are presented demonstrating different aspects of the proposed method.
Subject: Lyapunov functions; continuous and piecewise affine functions; computational techniques stability theory; ordinary differential equations
Identifier: http://hdl.handle.net/1959.13/1345469
Identifier: uon:29648
Identifier: ISSN:2158-2491
Language: eng
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