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

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 52; no. 12; pp. 7702 - 7713
• Main Authors: Zhang, Linchuang, Sun, Yonghui, Pan, Yingnan, Lam, Hak-Keung
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bandwidth; Circuits; Fault detection; Filter design (mathematics); Fuzzy semi-Markov jump systems (FSMJSs); Fuzzy systems; Markov processes; partly unknown transition rates (PUTRs); Quantization (signal); Reduced order filters; reduced-order fault detection filter design; Stability criteria; Symmetric matrices; Takagi-Sugeno model; Takagi–Sugeno (T–S) fuzzy method; Tunnel diodes
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2022.3163719

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.