考虑故障检测对象参数发生加性范数有界摄动的情况, 基于线性矩阵不等式(LMI)方法, 对一类由Delta算子描述的不确定离散故障检测系统的鲁棒$H_{\mathrm{\infty }}$故障检测滤波器设计问题进行研究.通过构建增广系统, 利用Lyapunov函数理论和Schur补定理, 把$H_{\mathrm{\infty }}$故障检测滤波器存在的充分条件转化为LMI形式.通过求解数值算例并作对比分析, 表明考虑对象参数发生摄动所设计的鲁棒$H_{\mathrm{\infty }}$ 故障检测滤波器能正确有效地检测到故障信号, 而不考虑对象参数发生摄动所设计的$H_{\mathrm{\infty }}$ 故障检测滤波器将不能正确有效地检测到故障信号.

With consideration that the parameters of the Delta operator-formulated uncertain discrete-time systems are of additively norm-bounded uncertainty, based on linear matrix inequality (LMI) method, a design method of robust $H_{\mathrm{\infty }}$ fault detection filter for the uncertain Delta operator-formulated discrete-time systems is discussed in this paper. By constructing an augmented system, with Lyapunov function theory and Schur complement lemma, a sufficient condition for the existence of the robust $H_{\mathrm{\infty }}$ fault detection filter is given in LMI form. A numerical example is used to illustrate the effectiveness of the proposed approach. The contrastive analysis results show that with the designed method, the fault signal can be correctly detected when the parameters of the fault detection systems are of variations, while the fault signal can't be correctly detected if the variations are not considered when the fault detection filter is designed.