Path-complete $p$-dominant switching linear systems

TL;DR

This paper introduces path-complete p-dominance for switching linear systems, generalizing slow mode analysis, characterized by quadratic cone contraction, enabling simplified dynamics analysis and an algorithm for verification.

Contribution

It presents the novel concept of path-complete p-dominance, linking it to quadratic cone contraction, and provides an algorithm to verify this property in switching systems.

Findings

Path-dominant systems exhibit low-dimensional dominant behavior.

The proposed algorithm effectively decides path-dominance.

Path-dominance generalizes slow mode analysis for switching systems.

Abstract

The notion of path-complete $p$-dominance for switching linear systems (in short, path-dominance) is introduced as a way to generalize the notion of dominant/slow modes for LTI systems. Path-dominance is characterized by the contraction property of a set of quadratic cones in the state space. We show that path-dominant systems have a low-dimensional dominant behavior, and hence allow for a simplified analysis of their dynamics. An algorithm for deciding the path-dominance of a given system is presented.