# Robust matrix commutator conditions for stability of switched linear systems under restricted switching

## TL;DR

This paper establishes new matrix commutator-based conditions for ensuring the stability of discrete-time switched linear systems with restricted switching, focusing on dwell times and subsystem activation patterns.

## Contribution

It introduces a novel approach using matrix commutators to derive stability conditions without Lyapunov functions, considering dwell time restrictions.

## Key findings

- Provides sufficient conditions for stability under dwell time constraints
- Characterizes stabilizing switching signals based on subsystem activation durations
- Avoids Lyapunov functions by using combinatorial matrix commutator analysis

## Abstract

This article treats global uniform exponential stability (GUES) of discrete-time switched linear systems under restricted switching. Given admissible minimum and maximum dwell times, we provide sufficient conditions on the subsystems under which they admit a set of switching signals that obeys the given restrictions on dwell times and preserves stability of the resulting switched system. Our analysis relies on combinatorial arguments applied to matrix commutators and avoids the employment of Lyapunov-like functions. The proposed set of stabilizing switching signals is characterized in terms of duration of activation of Schur stable subsystems and non-consecutive activation of distinct unstable subsystems.