Filtering for Fuzzy Systems With Multiplicative Sensor Noises and Multidensity Quantizer

Abstract

This paper considers the problem of I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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 I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. Finally, three examples are given to illustrate the developed new design techniques.