一类随机混杂系统的鲁棒方差控制

Robust Variance-constrained Control of a Class of Stochastic Hybrid Systems

对一类结构参数不完全已知的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(Linear matrix inequality,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.通过建立一个具有LMI约束的凸优化问题,给出了最小方差鲁棒控制器的设计方法.最后仿真结果表明了该方法的有效性.

The design of a state feedback robust variance controller is considered, which guarantees the closed-loop steady-state variance to be less than a given upper bound and concerns some H∞ performance for a class of Markov jump systems whose mode is not available completely. Based on linear matrix inequality （LMI） method, system variance is analyzed and the existence conditions 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. The problem of designing the minimum variance robust controller is formulated as a convex problem with LMI constrains. Finally, the simulation results show the effectiveness of the method proposed in this paper.