基于状态反馈的Markov切换随机时滞系统的均方指数稳定性

摘要

考察一类Markov切换时变时滞随机系统的均方指数稳定性.利用基于Liapunov函数和线性矩阵不等式的方法,给出了使状态反馈控制系统能克服不确定性和随机干扰,在均方意义下达到指数稳定的充分条件.当Markov链遍历所有模态时,给出了一个独立于Markov链模态集的增益矩阵,使得状态反馈控制系统均方指数稳定.%Exponential stabilization in mean square is investigated for a class of stochastic systems, where Markovian switching and time-varying delay is introduced. In order to guarantee the exponential stability in mean square for the system, a sufficient condition is derived using the method of Liapunov function and LMI. Furthermore, a kind of desirable gain matrix is designed to make the system the exponential stability in mean square by the state feedback. Finally, when the Markov chain goes around all its modes, a mode-independent gain matrix is presented to guarantee the exponential stability in mean square for this system.