Abstract

This paper presents new stability conditions for the continuous Takagi‐Sugeno (T‐S) fuzzy systems by using the Linear Matrix Inequality (LMI) approach. These new conditions are applied to design problems of fuzzy regulator. First, Takagi‐Sugeno fuzzy models and some stability results are recalled. To design fuzzy control systems, nonlinear systems are represented by Takagi‐Sugeno fuzzy models. The concept of parallel distributed compensation (PDC) is employed to design fuzzy controllers from the Takagi‐Sugeno fuzzy models. New stability conditions are obtained by relaxing the classical stability conditions. The stability conditions (classic and relaxed) of the closed‐loop system are expressed in terms of LMI. Design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the LMI procedures.

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