Path-complete positivity of switching systems

TL;DR

This paper introduces path-complete positivity for switched linear systems, generalizing positivity concepts using automata, and provides an algorithm for automatic verification of this property.

Contribution

It proposes the novel concept of path-complete positivity for switched systems and develops an algorithm for its automatic verification.

Findings

Path-complete positivity generalizes positivity to switched systems.

An algorithm for verifying path-positivity is developed.

Potential applications in stability analysis of switched systems.

Abstract

The notion of path-complete positivity is introduced as a way to generalize the property of positivity from one LTI system to a family of switched LTI systems whose switching rule is constrained by a finite automaton. The generalization builds upon the analogy between stability and positivity, the former referring to the contraction of a norm, the latter referring to the contraction of a cone (or, equivalently, a projective norm). We motivate and investigate the potential of path-positivity and we propose an algorithm for the automatic verification of positivity.