Stochastic stability of semi‐Markovian jump systems with mode‐dependent delays

TLDR

Semi‑Markovian jump systems, with time‑varying transition rates, can model a broader class of dynamical systems than conventional Markovian jump systems. The paper investigates stochastic stability of semi‑Markovian systems with mode‑dependent time‑variant delays. Using a Lyapunov function approach and piecewise analysis, a sufficient condition for stochastic stability is derived. The proposed condition is less conservative than existing results, and two examples demonstrate its effectiveness. © 2013 John Wiley & Sons, Ltd.

Abstract

SUMMARY Semi‐Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a class of semi‐Markovian systems with mode‐dependent time‐variant delays is investigated. By Lyapunov function approach, together with a piecewise analysis method, a sufficient condition is proposed to guarantee the stochastic stability of the underlying systems. As more time‐delay information is used, our results are much less conservative than some existing ones in literature. Finally, two examples are given to show the effectiveness and advantages of the proposed techniques. Copyright © 2013 John Wiley & Sons, Ltd.