# A new condition for stability of switched linear systems under restricted minimum dwell time switching

## TL;DR

This paper introduces a matrix commutator-based criterion for the stability of discrete-time switched linear systems with restricted minimum dwell time, providing robust conditions that generalize previous results for arbitrary switching.

## Contribution

It presents a new stability characterization using commutation relations, applicable under minimum dwell time constraints, extending prior arbitrary switching stability results.

## Key findings

- Derived sufficient stability conditions based on matrix commutators.
- Conditions are robust to small perturbations in subsystem matrices.
- Generalizes previous results for arbitrary switching to restricted dwell time cases.

## Abstract

We propose matrix commutator based stability characterization for discrete-time switched linear systems under restricted switching. Given an admissible minimum dwell time, we identify sufficient conditions on subsystems such that a switched system is stable under all switching signals that obey the given restriction. The primary tool for our analysis is commutation relations between the subsystem matrices. Our stability conditions are robust with respect to small perturbations in the elements of these matrices. In case of arbitrary switching (i.e., given minimum dwell time = 1), we recover the prior result [1,Proposition 1] as a special case of our result.