Performance analysis for cone-preserving switched systems with constrained switching

TL;DR

This paper develops performance analysis conditions for cone-preserving switched systems with constrained switching, generalizing existing results and providing new $$-performance criteria with practical insights.

Contribution

It introduces novel $$-performance analysis conditions for positive switched systems under constraints, unifying stability and performance analysis.

Findings

Generalized performance and stability analysis results for cone-preserving switched systems.

Derived new $$-performance conditions for systems with constrained switching.

Provided a numerical example demonstrating the application of the analysis.

Abstract

This paper studies cone-preserving linear discrete-time switched systems whose switching is governed by an automaton. For this general system class, we present performance analysis conditions for a broadly usable performance measure. In doing so, we generalize several known results for performance and stability analysis for switched and positive switched systems, providing a unifying perspective. We also arrive at novel $\ell_1$-performance analysis conditions for positive switched systems with constrained switching, for which we present an application-motivated numerical example. Further, the cone-preserving perspective provides insights into appropriate Lyapunov function selection.