Generalizing infinitesimal contraction analysis to hybrid systems

TL;DR

This paper extends infinitesimal contraction analysis to hybrid systems combining differential and difference equations, enabling global convergence insights for more complex systems.

Contribution

It introduces a novel theoretical framework that generalizes contraction analysis to hybrid systems, previously limited to smooth systems.

Findings

Theoretical generalization of contraction analysis to hybrid systems.

Illustrative examples demonstrating the applicability of the new framework.

Abstract

Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. Thus far, the technique has been restricted to systems governed by a single smooth differential or difference equation. We generalize infinitesimal contraction analysis to hybrid systems governed by interacting differential and difference equations. Our theoretical results are illustrated on a series of examples.