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arXiv · 2606.03797

Convergence of an algorithm for constructing Lyapunov functions for switched systems using meshfree collocation

Jay Ward·Nicos Georgiou·Peter Giesl
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Abstract

Switched systems are a class of dynamical systems where trajectories switch between different systems based on a switching rule. This rule can depend on time and/or the position of the trajectory in the state space. The existence of a Lyapunov function implies the existence of a uniformly asymptotically stable equilibrium point at the origin, which we prove in this paper. A method to construct Lyapunov functions for switched systems using meshfree collocation and quadratic programming was described in a related article. We prove that, under suitable assumptions, the algorithm described in this previous work converges as the fill distance between the collocation points tends to zero.

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Jay Ward, Nicos Georgiou, Peter Giesl. 2026-06-02. Convergence of an algorithm for constructing Lyapunov functions for switched systems using meshfree collocation. https://arxiv.org/abs/2606.03797

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