Relaxed nonfragile H∞ filter designs for T-S fuzzy systems

This paper deals with the problem of nonfragile H_∞ filter design for a class of discrete-time nonlinear systems that are represented by a Takagi-Sugeno (T-S) fuzzy models. New method of nonfragile H_∞ filter design is derived based on a relaxed approach in which both Finsler´s Lemma and delayed nonquadratic Lyapunov function are used. Compared with the existing results, more slack matrices are introduced in the design conditions which significantly enlarge the solution set of filter parameters. Moreover, conditions for the solvability of filter design given here are written in the form of linear matrix inequalities (LMIs) which can be efficiently solved by convex optimization techniques. An example is given to demonstrate the validity and applicability of the proposed approach.