This paper is concerned with the problem of finite frequency fault detection (FD) for a class of T-S fuzzy systems with partly unmeasurable premise variables. To fully use the available information of the considered T-S fuzzy system, an FD observer whose premise variables consist of the measurable premise variables and the estimations of unmeasurable ones of the fuzzy model is designed. However, the membership functions of the fuzzy model and the observer to be designed are unsynchronized, such that the existing FD methods based on parallel distribute compensation (PDC) strategy may be infeasible. To overcome this difficulty, a novel non-PDC $H_{\infty }/H_{-}$ unknown input observer is designed to achieve the purpose of fault detection and provide less conservative results. Finally, two simulation examples are given to illustrate the validity and merits of the presented FD scheme.

本文关注的是一类具有部分不可测前提变量的 TS 模糊系统的有限频率故障检测 (FD) 问题。为了充分利用所考虑的TS模糊系统的可用信息，设计了一个FD观察器，其前提变量由模糊模型的可测前提变量和不可测前提变量的估计组成。然而，模糊模型的隶属函数与待设计的观测器不同步，使得现有的基于并行分布补偿（PDC）策略的FD方法可能不可行。为了克服这个困难，一种新型的非 PDC$H_{\infty }/H_{-}$未知输入观测器旨在达到故障检测的目的，并提供较不保守的结果。最后，给出了两个仿真例子来说明所提出的 FD 方案的有效性和优点。