Computation of Lyapunov functions for systems with multiple attractors

Björnsson, Jóhann, Giesl, Peter, Hafstein, Sigurdur F and Kellett, Christopher M (2015) Computation of Lyapunov functions for systems with multiple attractors. Discrete and Continuous Dynamical Systems - Series A, 35 (9). pp. 4019-4039. ISSN 1078-0947

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Abstract

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.

Item Type: Article
Keywords: Lyapunov function, asymptotic stability, dynamical system, multiple local attractors, numerical method.
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Peter Giesl
Date Deposited: 16 Jun 2015 16:30
Last Modified: 07 Mar 2017 04:51
URI: http://sro.sussex.ac.uk/id/eprint/54584

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Project NameSussex Project NumberFunderFunder Ref
UnsetUnsetThe Icelandic Research FundUnset
UnsetUnsetAustralian Research Council Future FellowshipUnset