基于高阶PI观测器的不确定线性系统鲁棒故障检测设计

针对一类受干扰影响的不确定线性系统，研究了基于高阶比例积分 (proportional integral， PI)观测器的鲁棒故障检测设计问题。通过对一类Sylvester矩阵方程的参数化解，将基于高阶PI观测器的鲁棒故障检测问题转化为具有多约束的优化问题。基于该优化问题的解，给出了具有鲁棒故障检测功能的高阶PI观测器存在的充要条件，并给出受干扰影响的不确定线性系统的鲁棒故障检测设计方法。最后，数值算例及仿真分析结果验证了所提方法的有效性。

Design of robust fault detection in uncertain linear systems via high-order PI observers

The problem of designing robust fault detection via high order proportional integral (PI) obser vers in uncertain linear systems with disturbances is investigated. Based on the parametric solutions of a class of Sylvester matrix equations, the problem of designing robust fault detection via high order PI observers is changed into an optimal problem with multiple constraints. Based on the solution of the optimal problem, the necessary and sufficient existence condition of the high order PI observer with the robust fault detection function is derived, and a design method of robust fault detection in uncertain linear systems with disturbances is proposed. Finally, a numerical example and its simulation results show that the proposed method is effective.