Computation of Lyapunov functions for systems with multiple local attractors

DOI10.3934/dcds.2015.35.4019zbMath1366.37028OpenAlexW2065004693MaRDI QIDQ255801

Jóhann Björnsson, Peter Giesl, Christopher M. Kellett, Sigurður Freyr Hafstein

Publication date: 9 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2015.35.4019

zbMATH Keywords

numerical methodLyapunov functionasymptotic stabilitymultiple local attractor

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Lyapunov and storage functions (93D30) Stability of solutions to ordinary differential equations (34D20) Dynamics induced by flows and semiflows (37C10) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items

Computation and Verification of Lyapunov Functions, Asymptotic stability analysis of autonomous systems by applying the method of localization of compact invariant sets, Lyapunov function computation for autonomous systems with complex dynamic behavior, Automatic Determination of Connected Sublevel Sets of CPA Lyapunov Functions, Computation and verification of contraction metrics for exponentially stable equilibria, Computing complete Lyapunov functions for discrete-time dynamical systems, Minimization with differential inequality constraints applied to complete Lyapunov functions, Review on computational methods for Lyapunov functions

Uses Software

• GAIO
• RODES

Cites Work

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• Construction of Lyapunov functions for nonlinear planar systems by linear programming
• Linear programming based Lyapunov function computation for differential inclusions
• A rigorous ODE solver and Smale's 14th problem
• Revised CPA method to compute Lyapunov functions for nonlinear systems
• An algorithmic approach to chain recurrence
• On Liapounoff's conditions of stability
• Existence of complete Lyapunov functions for semiflows on separable metric spaces
• Distributed Algorithms for SCC Decomposition
• Providing a Basin of Attraction to a Target Region of Polynomial Systems by Computation of Lyapunov-Like Functions
• Lyapunov function construction for ordinary differential equations with linear programming
• Lyapunov functions and attractors in arbitrary metric spaces
• A smooth Lyapunov function from a class-${\mathcal{KL}}$ estimate involving two positive semidefinite functions
• Depth-First Search and Linear Graph Algorithms
• On the stability of solutions of a system of differential equations