Abstract: In view that the transition probability matrix (TPM) can only get part of the measurement data, the H control problem of discretetime Markov jump systems is considered by using an optimal estimation method. Firstly, an optimal estimation of TPM is obtained. Then, several sufficient existence conditions for modedependent H controllers are established in terms of linear matrix inequalities (LMIs). Comparing with the traditional results developed by the robust method, the proposed results in this paper are less conservative. Finally, the utility and superiority of the proposed method are verified by numerical examples.

Key words: Discretetime Markov jump system H control, Optimal estimation, Robust control, Linear matrix inequality

摘要： 针对转移概率矩阵只能得到若干观测值的实际情况, 研究离散 M a r k o v跳变系统的H¥ 控制问题。
首先利用最优化思想得到转移概率矩阵的一个最优估计。在此基础上, 以线性矩阵不等式的形式给出模态依赖H¥
控制器的求解条件, 与传统的鲁棒方法相比, 本文所提方法具有较小的保守性。最后通过数值算例验证所提方法的
有效性和优越性。

关键词:  离散 M a r k o v跳变系统, H¥, 控制, 最优估计, 鲁棒控制, 线性矩阵不等式