Robust Controller Design for Takagi–Sugeno Systems with Nonlinear Consequent Part and Time Delay

Abstract

This paper deals with the controller design problem for a class of delayed nonlinear systems by introducing a delayed Takagi–Sugeno system with nonlinear consequent parts. It is assumed that the fuzzy Takagi–Sugeno model contains disturbances or unstructured uncertainties. Depending on whether the system has input delay or not, two kinds of state-feedback controllers are supposed. By the help of Lyapunov–Krasovskii stability theory, some conditions in the form of linear matrix inequalities are presented such that the closed-loop system is asymptotically stable and achieves a prescribed \({\mathcal {H}}_\infty\) performance level. At the end, three examples are provided to illustrate the effectiveness of the proposed method.