posted on 2023-06-08, 21:10authored byJóhann 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