Continuous and Piecewise Affine Lyapunov Functions using the Yoshizawa Construction - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2014

Continuous and Piecewise Affine Lyapunov Functions using the Yoshizawa Construction

Abstract

We present a novel numerical technique for the computation of a Lyapunov function for nonlinear systems with an asymptotically stable equilibrium point. Our proposed approach constructs a continuous piecewise affine (CPA) function given a suitable partition of the state space, called a triangulation, and values at the vertices of the triangulation. The vertex values are obtained from a Lyapunov function in a classical converse Lyapunov theorem and verification that the obtained CPA function is a Lyapunov function is shown to be equivalent to verification of several simple inequalities. Furthermore, by refining the triangulation, we show that it is always possible to construct a CPA Lyapunov function. Numerical examples are presented demonstrating the effectiveness of the proposed method.
Fichier principal
Vignette du fichier
HKL13-Preprint.pdf (501.5 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00944393 , version 1 (10-02-2014)

Identifiers

Cite

Sigurđur Freyr Hafstein, Christopher M. Kellett, Huijuan Li. Continuous and Piecewise Affine Lyapunov Functions using the Yoshizawa Construction. American Control Conference (ACC), 2014, 2014, Portland, United States. pp.548 - 553, ⟨10.1109/ACC.2014.6858660⟩. ⟨hal-00944393⟩
66 View
189 Download

Altmetric

Share

Gmail Facebook X LinkedIn More