ℋ∞ Fuzzy Control for Systems with Repeated Scalar Nonlinearities

This paper is concerned with the H ∞ control problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with repeated scalar nonlinearities. A modified T-S fuzzy model is proposed in which the consequent parts are composed of a set of discrete-time state equations containing a repeated scalar nonlinearity. Such a model can describe some well-known nonlinear systems such as recurrent neural networks. Attention is focused on the analysis and design of ℋ∞ fuzzy controllers with the same repeated scalar nonlinearities such that the closedloop T-S fuzzy control system is asymptotically stable and preserves a guaranteed H ∞ performance. Sufficient conditions are obtained for the existence of admissible controllers, and the cone complementarity linearization (CCL) procedure is employed to cast the controller design problem into a sequential minimization one subject to linear matrix inequalities (LMIs), which can be solved efficiently by using existing optimization techniques. A illustrative example is provided to demonstrate the effectiveness of the results proposed in this chapter.