Probability-Based Robust H∞ Filtering for Time-Varying Systems with Randomly Occurring Gain Variations and Fading Channels

This paper is concerned with the non-fragile H-infinity filtering problem for a class of time-varying systems with randomly occurring gain variations (ROGVs), channel fading and probabilistic constraints. A set of mutually independent random variables with known probability distributions are introduced to describe the random parameter noises and randomly occurring parameter fluctuations during the filter implementation. Also, a stochastic Rice fading model is used to represent the channel fading of the system measurement, where the channel coefficients are a set of mutually independent random variables. The purpose of the addressed problem is to design a non-fragile time-varying filter to ensure the l(2) gain less than a prescribed level with probability constraints. By using the difference linear matrix inequalities (DLMIs) approach, two lemmas and two theorems are derived and the corresponding algorithms are proposed for both uniform distributed stochastic factors. Then the set of non-fragile time-varying filters, minimum H-infinity performance or maximum allowable probability are characterized by solving a convex problem via the semi-definite programming method. A simulation example including three cases is utilized to illustrate the effectiveness of the developed design scheme.