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.

Automated summary

This article addresses the fault detection problem for a class of T-S fuzzy semi-Markov jump systems with partly unknown transition rates subject to output quantization. A more general PUTRs model is constructed to describe the situation where some elements' information is completely unknown. The reduced-order filter is utilized to solve the fault detection problem, with the stochastic failure phenomenon injected into it. The logarithmic quantizer is employed to handle the limited bandwidth problem in the communication channel. New sufficient conditions based on the Lyapunov theory are developed to obtain the desired reduced-order filter.