Generalized Finite Frequency KYP Lemma and Applications to Fault Detection

Introduction

In the last two decades, fault detection has attracted considerable attention from many researchers due to the increasing demand for reliability and safety in industrial processes, for example [135, 188, 288]. Some results on fault detection in frequency domain have been reported in literatures, such as [1, 56, 302]. The effects of modeling disturbances and faults usually occupy in different frequency ranges. Therefore, designing an filter to detect the fault by satisfying rigorous performances in finite frequency domain is a key task in this topic. Though weighting functions [150] and frequency gridding [286] can deal with the finite frequency requirements. However, both of the two methods are hard to avoid computational burden and guarantee gain property performances simultaneously. With the aid of the generalized KYP Lemma, new LMI conditions were given for the finite frequency performance index [115, 119]. There are several results in the literature along this line, please refer to [116, 117, 118].