Dissipative Asynchronous Filtering for Networked Fuzzy Markov Jumping Systems With Quantized Measurements and Packet Dropouts

This article is concerned with the dissipative asynchronous filtering for a class of networked Takagi-Sugeno fuzzy Markov jumping systems subject to packet dropouts. The system measurements are quantized with a logarithmic quantizer and a Bernoulli model is introduced to deal with the packet dropouts occurred in the communication channel from the quantizer to the filter. Both the quantizer and the filter are mode dependent, and their modes are asynchronous with those of the physical plant, governed by two hidden Markov models. Based on the mode-and fuzzy-rule-dependent Lyapunov function method, a sufficient condition is derived such that the resultant filtering error system is stochastically stable in the mean-square sense and strictly dissipative. The slack-matrix approach and Finsler's lemma are further exploited to design suitable dissipative filters if a set of linear matrix inequalities are feasible. Finally, two examples including a tunnel-diode circuit system are taken to demonstrate the efficiency of our proposed results.

Automated summary

This article proposes a dissipative asynchronous filtering method for networked Takagi-Sugeno fuzzy Markov jumping systems subject to packet dropouts. It introduces a logarithmic quantizer for system measurements and a Bernoulli model for handling packet dropouts in the communication channel. Both the quantizer and the filter are mode dependent and governed by hidden Markov models. The article presents a condition for stochastically stable and strictly dissipative filtering error system using a Lyapunov function method and further designs suitable dissipative filters using the slack-matrix approach and Finsler's lemma if certain linear matrix inequalities are feasible. The efficiency of the proposed results is demonstrated through examples including a tunnel-diode circuit system.