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arXiv · 2606.02495

Construction of Lyapunov Functions for Switched Systems using Meshfree Collocation

Jay Ward·Nicos Georgiou·Peter Giesl
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Abstract

Switched systems are a family of dynamical systems where a switching rule indicates which system is "switched on". This rule can be dependent on time and/or position in the state space. Stability of switched systems is a property that is often investigated using the existence of one (or multiple) Lyapunov function(s). We develop an algorithm using a scattered approximation method to construct a Lyapunov function for switched systems, accompanied with stability results. The construction adapts a previous method for autonomous ODEs that uses meshfree collocation and quadratic programming.

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Jay Ward, Nicos Georgiou, Peter Giesl. 2026-06-01. Construction of Lyapunov Functions for Switched Systems using Meshfree Collocation. https://doi.org/10.1016/j.ifacol.2025.11.009

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