Invariance principles for switched systems with restrictions

TL;DR

This paper develops invariance principles for switched nonlinear systems with restrictions, providing new stability criteria for systems with constrained switching logic and memory-dependent switching behavior.

Contribution

It introduces invariance principles tailored for switched systems with restrictions and derives stability conditions using observability-like notions.

Findings

Established invariance principles for constrained switched systems

Derived convergence and stability criteria for systems with memory-dependent switching

Enabled stability analysis of systems with state-dependent switching constraints

Abstract

In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these systems and derive by using observability-like notions some convergence and asymptotic stability criteria. These results enable us to analyze the stability of solutions of switched systems with both state-dependent constrained switching and switching whose logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems.