Contraction analysis of switched Filippov systems via regularization

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.

Preprint submitted to Automatica

References in corpus (2)

• Switching control for incremental stabilization of nonlinear systems via contraction theory
• Contraction and incremental stability of switched Carathéodory systems using multiple norms

Cited by in corpus (4)

• Observer design for piecewise smooth and switched systems via contraction theory
• Technical Report: Optimal Control of Piecwise-smooth Control Systems via Singular Perturbations
• Robust Contraction Analysis of Nonlinear Systems via Differential IQC
• Vector Contraction Analysis for Nonlinear Dynamical Systems