In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.

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Fuzzy models have received particular attention in the area of nonlinear modeling, especially the Takagi-Sugeno (TS) fuzzy models, due to their capability to approximate any nonlinear behavior. The performances of a TS fuzzy model depend on its complexity (Number of fuzzy rules), on the type of membership functions and also on antecedent variables and consequent regressors. In the first part of this paper we describe an algorithm for TS fuzzy modeling. The main idea is to select antecedent variables independently of consequent regressors in order to identify a "best" TS fuzzy model. In the second part we discuss the use of TS fuzzy models to design a fuzzy predictive controller. Predictive control has been first developed to control Linear Time Invariant (LTI) plants, described by Auto Regressive Moving Average with eXternal inputs (ARIMAX) models. The extension of this control strategy in the case when the behavior of the plant is non linear and modeled by a Takagi-Sugeno fuzzy model is considered here. This kind of nonlinear model is locally linear and the GPC technique can be extended as a parallel distributed controller.