Fuzzy robust H<sub>∞</sub> control for uncertain nonlinear systems with multiple delays

Abstract

The problem of the fuzzy H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> state feedback control for a class of uncertain nonlinear systems with time-varying input and multiple state delays is addressed in this paper. The Takagi-Sugeno (T-S) model with time-delay and parameter uncertainties is adopted for modelling nonlinear systems. Using PDC method and Lyapunov functional method, the systematic design procedure for the fuzzy robust controller is presented in the form of linear matrix inequalities (LMIs). A sufficient condition is derived for the existence of fuzzy H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> state feedback controller which guarantees the closed-loop system is asymptotically stable and the effect of the disturbance input on controlled output is reduced to a prescribed level. Finally, an example is given to demonstrate the effectiveness of the proposed method.