乘性Markov跳变系统鲁棒方差控制

Robust variance-constrained H_∞ control for Markov jump system with multiplicative noise

针对一类具有乘性噪声和参数不确定性的Markov跳变参数系统,研究使得闭环系统的稳态状态方差小于某个给定的上界,同时满足一定H∞性能的状态反馈鲁棒方差控制器设计问题.运用线性矩阵不等式(LMI)方法,对系统进行了方差分析,给出并证明了控制器存在的条件,进而用一组线性矩阵不等式的可行解给出了控制器的一个参数化表示.最后的仿真结果验证了该方法的有效性.

For Markov jump linear system with multiplicative noise and uncertainties,the design problem of state feedback robust variance controller is researched which guarantees the closed-loop steady-state variance to be less than a given upper bound and some H∞ performances are concerned. Based on linear matrix inequality （LMI） method,system variance is analyzed and conditions for the existence of such controllers are proposed and proved. A parameterized representation of a set of desired controllers is characterized in terms of the feasible solutions to the LMI system. Finally,the simulation results show the effectiveness of the proposed method.