广义转移速率条件下连续时间奇异Markov跳变系统的随机容许性分析

Stochastic Admissibility of Continuous-time Singular Markov Jump Systems with General Uncertain Transition Rates

针对一类连续时间奇异Markov跳变系统,研究了其随机容许性的问题。首先,引入广义转移速率的概念,同时给出了该类奇异Markov跳变系统正则、无脉冲、随机稳定的充分性判据;其次,对广义转移速率进行分类处理,利用严格线性矩阵不等式和Schur补理论得出系统随机容许性的充分条件;最后,设计状态反馈控制器,确保系统满足随机容许性,并给出系统状态反馈矩阵表示形式。

This paper is devoted to studying the stochastic admissibility for a class of continuous-time singular Markov jump systems. Firstly, the concept of general uncertain transition rates was introduced and the sufficient criteria for the regular, impulse-free and stochastic stability of the systems were presented. Secondly, the general uncertain tran- sition rates were classified and the sufficient conditions for stochastic admissibility was obtained with the aid of Schur＇s complement and a set of strict linear matrix inequalities. Finally,a state feedback controller was designed to guarantee the stochastic admissibility of the systems and the system state feedback matrix representation was given.