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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