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Automatic determination of connected sublevel sets of CPA Lyapunov functions

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posted on 2023-06-09, 20:14 authored by Peter GieslPeter Giesl, Conor Osborne, Sigurdur Hafstein
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

SIAM Journal on Applied Dynamical Systems (SIADS)

ISSN

1536-0040

Publisher

Society for Industrial and Applied Mathematics

Issue

2

Volume

19

Page range

1029-1056

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2020-01-14

First Open Access (FOA) Date

2020-05-05

First Compliant Deposit (FCD) Date

2020-01-13

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