Applications of fuzzy control to nonlinear time-delay systems using the linear matrix inequality fuzzy Lyapunov method

This study proposes a kind of fuzzy robustness controller design for nonlinear time-delay systems based on the fuzzy Lyapunov method, which is defined in terms of fuzzy blending quadratic Lyapunov functions. The basic idea is to construct the Takagi-Sugeno fuzzy model and fuzzy controller for nonlinear dynamic systems with disturbances in which the stability criterion is derived in terms of the fuzzy Lyapunov method. Based on the robustness design and parallel distributed compensation scheme, the problems of modeling errors between real dynamic systems and T-S models are solved. Furthermore, the presented condition is transformed into linear matrix inequalities making it numerically feasible to find the fuzzy state feedback gain and common solutions with the Matlab toolbox. The proposed method is illustrated for a nonlinear chaotic time-delay system and the simulation results show that the robustness controller cannot only stabilize the nonlinear chaotic system, but also has robustness against external disturbances. The simulation is provided to explore the feasibility of the proposed fuzzy controller design method.