Nonfragile $H_{\infty}$ Fuzzy Filtering With Randomly Occurring Gain Variations and Channel Fadings

Abstract

This paper is concerned with the nonfragile H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with both randomly occurring gain variations (ROGVs) and channel fadings. the phenomenon of the ROGVs is introduced into the system model so as to account for the parameter fluctuations occurring during the filter implementation. Two sequences of random variables obeying the Bernoulli distribution are employed to describe the phenomenon of the ROGVs bounded by prescribed norms. In addition, the Rice fading model is utilized to describe the phenomena of channel fadings, where the occurrence probabilities of the random channel coefficients are allowed to time varying. Through stochastic analysis and Lyapunov functional approach, sufficient conditions are established under which the filtering error dynamics is exponentially mean-square stable with a prespecified H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. The set of the desired nonfragile H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters is characterized by solving a convex optimization problem via the semidefinite programming method. An illustrative example is given to show the usefulness and effectiveness of the proposed design method in this paper.