Reduced-Order Fault Detection Filter Design for Fuzzy Semi-Markov Jump Systems With Partly Unknown Transition Rates

This article deals with the fault detection problem for a class of Takagi–Sugeno (T–S) fuzzy semi-Markov jump systems (FSMJSs) with partly unknown transition rates (PUTRs) subject to output quantization by designing a reduced-order filter. First, a more general PUTRs model is constructed to describe the situation that the information of some elements is completely unknown, where this model is affected simultaneously by PU information and time-varying parameter compared with the traditional PUTRs model. Second, we take full advantage of the reduced-order filter to address the fault detection problem for FSMJSs, in which the stochastic failure phenomenon is injected into the reduced-order filter. Besides, the logarithmic quantizer is employed to tackle the limited bandwidth problem in a communication channel. Consequently, the new sufficient conditions are developed based on the Lyapunov theory to obtain the desired reduced-order filter. Simulation results with respect to the tunnel diode circuit are provided to demonstrate the usefulness and availability of the established theoretical results.