Sufficient Lyapunov conditions for exponential mean square stability of discrete-time systems with markovian delays (extended version)

TL;DR

This paper develops Lyapunov-based criteria to ensure exponential mean square stability in discrete-time systems with Markovian delays, transforming the problem into a Markov jump system framework.

Contribution

It extends existing Lyapunov conditions from delay digraphs to Markovian delays, providing a new approach for stability analysis of such systems.

Findings

Successfully transforms systems with Markovian delays into Markov jump systems.

Provides sufficient Lyapunov conditions for exponential mean square stability.

Demonstrates the method's effectiveness through an illustrative example.

Abstract

This paper introduces sufficient Lyapunov conditions guaranteeing exponential mean square stability of discrete-time systems with markovian delays. We provide a transformation of the discrete-time system with markovian delays into a discrete-time Markov jump system. Then, we extend sufficient Lyapunov conditions existing for the global asymptotic stability of discrete-time systems with delays digraphs to the mean square stability of discrete-time systems with markovian delays. Finally, an example is provided to illustrate the efficiency and advantage of the proposed method.