Fuzzy controller design for nonlinear uncertain system with time delay based on LMI approach

In this paper, Takagi-Sugeno (T-S) fuzzy model approach is exploited to establish stability criteria for a class of nonlinear uncertain systems with time delay. The T-S fuzzy model is used to describe a nonlinear uncertain system in terms of fuzzy sets and fuzzy reasoning applied to a set of linear sub models. Moreover the system is considered in two conditions: the upper bound of the disturbance is known and that unknown, respectively. In terms of Lyapunov's direct method for multiple time-delay fuzzy interconnected systems, a novel linear matrix inequalities (LMIs) will be utilized to solve the problem. Finally, the proposed methodology is illustrated by an example of a nonlinear system with time-delay.