Filtering for Fuzzy Systems With Multiplicative Sensor Noises and Multidensity Quantizer

This paper considers the problem of <inline-formula><tex-math notation="LaTeX">$l_2-l_\infty$</tex-math></inline-formula> filtering for discrete-time Takagi–Sugeno (T–S) fuzzy systems with multiplicative sensor noises over the channels with limited capacity. A more general multidensity logarithmic quantizer is designed to increase the utilization of the communication resources, and a sojourn-time-dependent Markov chain is used to model the variation of the quantizer density. Then, the fuzzy basis-, quantizer density-, and sojourn-time-dependent filter is designed for T–S fuzzy systems on the basis of the quantized measurements to improve the performance of the filter. Sufficient conditions are proposed to guarantee that the filtering error system is exponentially mean-square stable and achieves a prescribed <inline-formula><tex-math notation="LaTeX">$l_2-l_\infty$</tex-math></inline-formula> performance. Finally, three examples are given to illustrate the developed new design techniques.

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