马尔可夫时滞网络控制系统的稳定性

Stability of networked control systems with time-delays governed by Markov chains

针对同时具有马尔可夫(Markov)链跳变特性时滞和随机丢包现象的网络控制系统,建立了网络控制系统的离散模型,利用李亚普诺夫稳定性理论、线性矩阵不等式和自由权矩阵方法,分析了系统的均方稳定性和均方可镇定性,并基于线性不等式给出了系统均方稳定、镇定判据.该方法能判定具有马尔可夫时滞和丢包的网络控制系统的均方稳定性,并设计出同等条件下的均方可镇定时滞依赖控制器.与现有方法相比,能更准确地描述网络时滞特性,有效减小系统保守性,结果更具一般性.最后通过仿真实例证明了方法的有效性.

Networked control systems （NCSs） with time-varying delay governed by Markov chains and stochastic packet dropout are considered. A discrete time model of NCSs is proposed. Mean square stability and stabilization of the system are analyzed by Lyapunov stability theory combined with linear matrix inequalities techniques and free-weighting matrices technique. Some mean square stability and stabilization criteria are also derived. Using this proposed method, we are able to analyze mean square stability of NCSs with Markovian delay and stochastic packet dropout, and design delay-dependent controller satisfied mean square stabilization. Compared with reported methods, the proposed methods can describe properties of time delay in real network accurately, giving a much less conservative delay bound and more general results. The validity of the developed theory is testified by the numerical examples and simulation.