一类具有随机时滞的受扰马尔科夫跳变系统有限时间稳定性

Finite-time stability for a kind of Markovian jump systems subject to random delays and external disturbances

本文研究了一类具有随机时滞的受扰马尔科夫跳变线性系统的有限时间稳定性问题.通过引入服从伯努利分布的随机变量刻画了时滞变化的随机特性.本文首先分析了系统的随机有限时间稳定性,基于分析结果设计了反馈控制器,使得系统状态在马尔科夫跳变、随机时滞和外界扰动等并存时,在给定时间内收敛于某一区域而不超过指定的上界值,并可获得该上界的具体值.最后通过数值仿真验证了所提算法的有效性.

This paper addressed the stochastic finite-time stability（ SFTS） problem for a class of Markovian jump systems with random delays and external disturbances. Stochastic variables obeying Bernoulli distribution are introduced to model the random delays. In this work,firstly,SFTS performances are analyzed. Based on these analyses,new criteria are derived to synthesize the SFTS controller,such that system states are SFTS in the presence of Markov jumps,time delays,and external disturbances. Besides,the upper bound of state values is derived in an explicit form.Finally,an illustrative example is provided to verify the effectiveness of the proposed algorithm.