An Approach to Fault Detection for Multirate Sampled-Data Systems With Frequency Specifications

This paper is concerned with the design of fault detection for sampled-data systems, which are based on multirate sampling, with frequency specifications. A general multirate system is considered in this paper, where not only the inputs and outputs but also their different channels have different sampling rates. The purpose of this paper is to make this residual system with multirate sampling satisfy a given disturbance attenuation level over a restricted frequency range. With the use of the lifting technique, this paper reformulates a single-rate linear time-invariant system, which is equivalent to the multirate time-varying system. For a given restricted frequency range, convex conditions are obtained in designing a required fault detection filter. Then, the restricted frequency ranges problem are also solved specifically via the generalized Kalman-Yakubovic̆-Popov lemma. Finally, this paper uses a continuous-stirred tank reactor system to illustrate the effectiveness and advantages of the fault detection filter design method.