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This paper deals with the stability analysis of Takagi-Sugeno models (T-S). Based on a piecewise quadratic Lyapunov functions and the use of the so-called Sprocedure, new asymptotic stability conditions for both continuous and discrete T-S models are presented. The stability conditions are formulated in linear matrix inequalities (LMIs). Examples are given to i h t r a t e the advantage of the proposed method.Keywords: T-S model, nonlinear models, stability analysis, Lyapunov methods, S-procedure, LMIs. discontinuous. A polyquadratic Lyapunov function which is built on the same basis as the T-S model itself is studied for continuous case [1][3][7][11][18]. Using convex optimization, this type of Lyapunov function is also computed for discrete systems with time varying uncertainties [6]. In Linear Parameter Varying (LF'V) systems, to reduce the conservativeness, quadratic parameter dependant Lyapunov functions are used [2O]-[23]. The LPV systems may also be represented by T-S models. However, the way which consist to embed nonlinear systems into LPV framework, i.e. when the states are viewed as time varying parameter, will lead obviously to conservative results [I].

This paper studies the design of a static output feedback controller for nonlinear systems described by multiple model approach. Motivated by quadratic stabilization result developed for parallel distributed compensation (PDC) controller, an Output PDC (OPDC) controller that corresponds to a nonlinear static output feedback control law is proposed. Both stabilization and pole placement are addressed, firstly by a cone complementarity formulation of the problem and secondly by transformation to linear matrix inequality (LMI) problem. An example is given to illustrate the results.