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Computation of Lyapunov functions for systems with multiple attractors

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posted on 2023-06-08, 21:10 authored by Jóhann Björnsson, Peter GieslPeter Giesl, Sigurdur F Hafstein, Christopher M Kellett
We present a novel method to compute Lyapunov functions for continuous-time systems with multiple local attractors. In the proposed method one first computes an outer approximation of the local attractors using a graphtheoretic approach. Then a candidate Lyapunov function is computed using a Massera-like construction adapted to multiple local attractors. In the final step this candidate Lyapunov function is interpolated over the simplices of a simplicial complex and, by checking certain inequalities at the vertices of the complex, we can identify the region in which the Lyapunov function is decreasing along system trajectories. The resulting Lyapunov function gives information on the qualitative behavior of the dynamics, including lower bounds on the basins of attraction of the individual local attractors. We develop the theory in detail and present numerical examples demonstrating the applicability of our method.

Funding

Australian Research Council Future Fellowship

The Icelandic Research Fund

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Discrete and Continuous Dynamical Systems - Series A

ISSN

1078-0947

Publisher

American Institute of Mathematical Sciences

Issue

9

Volume

35

Page range

4019-4039

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2015-06-16

First Open Access (FOA) Date

2017-01-17

First Compliant Deposit (FCD) Date

2017-01-17

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