Automatic determination of connected sublevel sets of CPA Lyapunov functions

Giesl, Peter, Osborne, Conor and Hafstein, Sigurdur (2020) Automatic determination of connected sublevel sets of CPA Lyapunov functions. SIAM Journal on Applied Dynamical Systems (SIADS), 19 (2). pp. 1029-1056. ISSN 1536-0040

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Abstract

Lyapunov functions are an important tool to determine the basin of attraction of equilibria. In particular, the connected component of a sublevel set, which contains the equilibrium, is a forward invariant subset of the basin of attraction. One method to compute a Lyapunov function for a general nonlinear autonomous differential equation constructs a Lyapunov function, which is continuous and piecewise affine (CPA) on each simplex of a fixed triangulation. In this paper we propose an algorithm to determine the largest connected sublevel set of such a CPA Lyapunov function and prove that it determines the largest subset of the basin of attraction that can be obtained by this Lyapunov function.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Amelia Redman
Date Deposited: 14 Jan 2020 08:36
Last Modified: 18 Sep 2020 09:29
URI: http://sro.sussex.ac.uk/id/eprint/89330

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