Contraction analysis of switched Filippov systems via regularization

TL;DR

This paper develops a contraction-based approach to analyze the stability and convergence of switched Filippov systems, including PWS, PWA, and relay feedback systems, using regularization techniques and non-Euclidean metrics.

Contribution

It introduces new sufficient conditions for trajectory convergence in Filippov systems using regularization, extending analysis beyond Euclidean metrics.

Findings

Conditions ensure convergence of trajectories in Filippov systems.

Applicable to PWS, PWA, and relay feedback systems.

Numerical simulations confirm effectiveness and ease of application.

Abstract

We study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems, we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that contrary to previous approaches, our conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application.