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This paper presents new relaxed stability conditions and LMI-(linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. They are applied to design problems of fuzzy regulators and fuzzy observers. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy regulators and fuzzy observers, nonlinear systems are represented by Takagi-Sugeno's (T-S) fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the T-S fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. LMIbased design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions. Other LMI's with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures. Design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the LMI-based design procedures.

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This paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems. First, a stability condition for Takagi and Sugeno's fuzzy model is given in terms of Lyapunov stability theory. Next, new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization, H w control theory, and linear matrix inequalities. The derived stability conditions are used to analyze the stability of Takagi and Sugeno's fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems. The design method employs the so-called parallel distributed compensation. Important issues for the stability analysis and design are remarked. Finally, three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented.

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