# Necessary and Sufficient Conditions for Stability of Discrete-Time Switched Linear Systems with Ranged Dwell Time

arXiv: https://arxiv.org/abs/2105.14113 · HTML: https://mlsanity.com/paper/2105.14113/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2021.

## Built on by (most cited first, 1 of 1)

- [Towards Safe Path Tracking Using the Simplex Architecture](https://mlsanity.com/paper/2503.10559/) (2025)

## Abstract (arXiv)

This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying the prescribed ranged dwell time constraint. Based on L-switching-cycle, two sufficient conditions are proposed to ensure the global uniform asymptotic stability of discrete-time switched linear systems. It is noted that two conditions are equivalent in stability analysis with the same L-switching-cycle. These two sufficient conditions can be viewed as generalizations of the clock-dependent Lyapunov and multiple Lyapunov function methods, respectively. Furthermore, it has been proven that the proposed L-switching-cycle can eventually achieve the nonconservativeness in stability analysis as long as a sufficiently long L-switching-cycle is adopted. A numerical example is provided to illustrate our theoretical results.