Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability, H-infinity control theory, and linear matrix inequalities

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-infinity 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.