Fuzzy Filtering With Randomly Occurring Parameter Uncertainties, Interval Delays, and Channel Fadings

In this paper, the
$H_{\infty}$
fuzzy filtering problem is investigated for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with randomly occurring uncertainties and randomly occurring interval time-varying delays, as well as channel fadings. A sequence of random variables obeying the Bernoulli distribution is utilized to govern the randomly occurring uncertainties and probabilistic interval time-varying delays. Simultaneously, the Rice fading model is employed to describe the phenomena of channel fadings by setting different values of the channel coefficients. Our attention is focused on the design of an
$H_{\infty}$
fuzzy filter such that the filtering error dynamics is exponentially mean-square stable and the disturbance rejection attenuation is constrained to a given level by means of the
$H_{\infty}$
-performance index. In the presence of the randomly occurring phenomena, sufficient conditions are derived, via stochastic analysis and Lyapunov functional approach, for the existence of desired filter ensuring both the exponential mean-square stability and the prescribed
$H_{\infty}$
performance. The filter parameters can be obtained by solving a convex optimization problem via the semidefinite program method. Finally, a numerical example is utilized to illustrate the usefulness and effectiveness of the proposed design technique.