The reachable set synthesis problem of singular Markovian jump systems (SMJSs) is investigated in this paper. Both state reachable set and output reachable set are considered for SMJSs without delay and with distributed delay. By utilizing proportional and derivative state feedback control technique, sufficient conditions for delay-free SMJSs are proposed to guarantee the reachable set of closed-loop systems to be mean-square bounded by a prescribed ellipsoid firstly. Then the result is extended to SMJSs with distributed delay. Numerical examples are given to demonstrate the effectiveness of the obtained result.

中文翻译：

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奇异马尔可夫跳跃系统的可到达集合综合

研究了奇异马尔可夫跳跃系统（SMJSs）的可达集综合问题。对于SMJS，无延迟且具有分布式延迟都考虑了状态可达集和输出可达集。通过利用比例和微分状态反馈控制技术，提出了无延迟SMJS的充分条件，以确保闭环系统的可到达集合首先是由规定的椭球界定的均方。然后将结果扩展到具有分布式延迟的SMJS。数值例子说明了所得结果的有效性。