离散切换系统的H＿／H∞故障检测滤波器设计

摘要

为解决离散时间线性切换系统的故障检测问题，设计了满足混合H＿／H∞性能指标的鲁棒故障检测滤波器。首先，通过构造故障检测滤波器来得到残差，并且为提高故障检测的性能，使用加权H∞性能指标和H＿性能指标表示残差对于扰动的鲁棒性以及对于故障的敏感性，进而将鲁棒故障检测滤波器的设计问题转化为混合H＿／H∞性能指标下的多目标求解问题。接着，利用多Lyapunov函数方法和平均驻留时间技术，先得到了初步的滤波器设计结果，然后通过引入松弛变量的方法解除了Lya⁃punov矩阵和系统矩阵的耦合，得到了保守性较低的结果，并将其表示为线性矩阵不等式形式。最后，使用一个例子进行仿真，为其设计了故障检测滤波器的参数矩阵，并得到了残差评价函数的仿真图形。仿真结果表明，所设计的故障检测滤波器可以实现故障检测的功能。%The fault detection problem of discrete time linear switched system is studied by using the robust fault detection filter in the framework of mixed H_/H∞. First of all, residual is obtained by constructing fault detection filter. For the purpose of improving the accuracy of fault detection, weighted H∞ performance is used as the robustness indicator of residual to disturbance, and H_ performance is regarded as the sensitivity indicator of residual to fault. As a result, the problem of robust fault detection filter design is converted to a multi⁃objective solving problem under the mixed H_/H∞. performance index. Then, multiple Lyapunov functions and average dwell time approach are used for deriving the preliminary result of filter design. Moreover, the couple between Lyapunov matrix and system matrix is removed by introducing the slack variables, and less conservative results are obtained. All results are in the form of linear matrix inequality. Finally, a numerical example that the parameters of the fault detection filter are designed is given to show that the designed filter can realize the function of fault detection.