$H_\infty$ Fuzzy Control With Randomly Occurring Infinite Distributed Delays and Channel Fadings

Abstract

In this paper, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> output-feedback control problem is investigated for a class of discrete-time fuzzy systems with randomly occurring infinite distributed delays and channel fadings. A random variable obeying the Bernoulli distribution is introduced to account for the probabilistic infinite distributed delays. The stochastic Rice fading model is employed to simultaneously describe the phenomena of random time delays and channel fadings via setting different values of the channel coefficients. The aim of this paper is to design an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> output-feedback fuzzy controller such that the closed-loop Takagi-Sugeno (T-S) fuzzy control system is exponentially mean-square stable, and the disturbance rejection attenuation is constrained to a given level by means of the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index. Intensive analysis is carried out to obtain sufficient conditions for the existence of desired output-feedback controllers, ensuring both the exponential mean-square stability and the prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. The cone-complementarity linearization algorithm is utilized to cast the controller design problem into a sequential minimization: one that is solvable by the semi-definite programming method. A simulation result is exploited to illustrate the usefulness and effectiveness of the proposed design technique.