Non-fragile H∞ filtering for delayed Takagi-Sugeno fuzzy systems with randomly occurring gain variations

In this study, we consider a non-fragile H∞ filter design for a class of continuous time delayed Takagi-Sugeno (T-S) fuzzy systems. The filter design is assumed to include randomly occurring gain variations according to the filter's implementation. Two independent Bernoulli distributions are employed to describe these random phenomena. We focus mainly on the design of a non-fragile filter so the filtering error system is asymptotically mean-square stable with the prescribed H∞ performance in the presence of both randomly occurring gain variations and a time delay. A sufficient condition is developed by employing the Lyapunov functional approach. Based on this condition, an improved H∞ filter for delayed T-S fuzzy system is described, which is free of randomly occurring gain variations. The filter parameters are obtained by solving a set of linear matrix inequalities. The effectiveness and the advantages of the proposed techniques are demonstrated by two numerical examples.