Non-fragile H∞H∞ filtering for nonlinear systems with randomly occurring gain variations and channel fadings

In this paper, the H∞H∞ filtering problem is addressed for a class of discrete-time stochastic systems subject to randomly occurring gain variations (ROGVs), channel fadings, as well as randomly occurring nonlinearities (RONs). Due to the random nature of the occurrence of the gain variations in actual implementation, ROGVs, to be regulated by a group of random variables with Gaussian distribution, are utilized to better reflect this phenomenon. Then a L  -th Rice fadings model is employed to represent channel fadings and time-delays simultaneously, in which the channel coefficients are mutually independent random variables conforming to any probability density function on [0, 1]. Furthermore, a kind of stochastic nonlinear disturbance is also considered in the H∞H∞ filtering research by means of a Bernoulli distributed white sequence. The purpose of this paper is to devise a non-fragile H∞H∞ filter such that the overall error dynamics is stochastically stable and satisfies the prescribed H∞H∞ performance. Through the Lyapunov stability theory, intensive stochastic analysis along with LMI methods, sufficient conditions are set up for the desired stochastic stability and H∞H∞ disturbance attenuation, and the proposed non-fragile filtering problem is converted into solving a convex optimization problem by the semidefinite programming technique. Finally, a numerical simulation example is provided to illustrate the effectiveness of the proposed design approach.