中文摘要：

考虑未知输入信号的影响，研究了线性系统鲁棒故障检测观测器的设计问题。利用描述残差对故障灵敏度的H_指数和表示残差对未知输入鲁棒性的H∞范数，将鲁棒故障检测观测器的设计问题描述为基于H_／H∞的优化设计问题。利用线性矩阵不等式（linear matrix inequality，LMI）理论，给出故障检测观测器的存在条件，提出一种新的迭代LMI算法求解最优观测器增益。仿真结果表明，利用这种方法设计的故障检测观测器对故障的灵敏度高，对未知输入的鲁棒性强。

英文摘要：

Considering the effect of unknown input signals, the problem of a robust fault detection observer design for linear uncertain systems is investigated. The H_index and the H∞ norm, which measure the sensitivi- ty of the residual to the fault and the robustness of the effect of the unknown input on the residual, respectively, are used to describe the problem of this observer design as optimization problems. The existence conditions of such a fault detection observer are given in terms of matrix inequalities. The optimization observer gain is ob- tained by a new iterative linear matrix inequality （LMI） algorithm. The given example demonstrates that the de- signed fault detection observer has high sensitivity to the fault and strong robustness to the unknown input.