An H_∞ approach to fault detection for multirate sampled-data systems with frequency specifications

The target of the article is to solve the problem of fault detection for a multirate sampled-data system with frequency specifications. And the multirate condition considered in this article is that different channels of both the inputs and the outputs have different sampling rates. This paper aims to solve this fault detection problem with using a fault detection filter to make the residual system satisfy a given disturbance attenuation level over a restricted frequency range. The problem is solved via reformulating the multirate sampled-data system with extended inputs and outputs and utilizing the generalized Kalman-Yakubovič-Popov lemma to deal with the restricted frequency specifications. Finally, we use an example to illustrate the design procedure and show the advantages of the proposed method.