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研究一类随机Markov跳跃系统的稳定性与镇定控制问题.此类系统跳跃过程的转移概率部分未知,包括转移概率完全已知和完全未知两种情形,因而更具一般性.首先,给出保证随机Markov跳跃系统均方渐近稳定的充分性判据,并设计了相应的状态反馈镇定控制器;然后,基于矩阵的奇异值分解给出了系统静态输出反馈镇定控制器的设计方法,并将其归结为求解一组线性矩阵不等式(LMIs)的可行性问题;最后,通过数值仿真验证了所得结论的正确性.
In this paper, we study the stability and stabilization control problems of a class of stochastic Markov jump systems. The transition probability of such a system jump process is unknown, including the transition probability is completely known and completely unknown, so it is more general.First, Then the sufficient condition for the existence of mean square asymptotic stability of stochastic Markov jump systems is obtained and the corresponding state feedback stabilization controller is designed. Then, the design method of the system static output feedback stabilization controller is given based on matrix singular value decomposition. It comes down to the feasibility of solving a set of linear matrix inequalities (LMIs). Finally, the correctness of the conclusion is verified by numerical simulation.