Robustness design of time-delay fuzzy systems using fuzzy Lyapunov method

In this study we address a fuzzy Lyapunov method for the stability analysis of time-delay fuzzy systems subject to external disturbances. A Takagi–Sugeno (T–S) fuzzy model and parallel distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy controller for the stabilization of time-delay fuzzy systems. According to the controlled system, the H∞ criterion is derived based on the fuzzy Lyapunov method, which is defined in terms of fuzzy-blending quadratic Lyapunov functions. Based on the stability criterion, the time-delay fuzzy systems are guaranteed to be stable. The control problem can then be reformulated as a linear matrix inequality (LMI) problem. A simulation is provided to explore the feasibility of the proposed fuzzy controller design method.