Fault Detection in Finite Frequency Domain for Networked Multi-Rate Systems under Stochastic Communication Protocol

This paper deals with the problem of fault detection (FD) in finite frequency domain for networked multi-rate systems (NMSs) with logarithmic quantization under the stochastic communication protocol (SCP). First, consider a class of NMSs where the output sampling period is an integer multiple of the input. To reduce the communication burden of the network and the occurrence of data collisions, the quantized measurement outputs are transmitted via the SCP, which is governed by a discretetime Markov chain. NMSs are converted into networked single-rate systems by using the lifting technique, and then the residual system model for the filter-based FD is established. The purpose of this paper is to design a FD filter satisfying disturbance attenuation level in a restricted frequency domain. Then, the sufficient conditions for this problem are derived by using the generalized Kalman-Yakubovich-Popov (GKYP) lemma and expressed in the form of linear matrix inequalities (LMIs). Finally, an example is employed to illustrate the effectiveness of the proposed method.