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Robustness design of time-delay fuzzy systems using fuzzy Lyapunov method. (English) Zbl 1152.93040

Summary: 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 a parallel distributed compensation scheme are first employed to design a nonlinear fuzzy controller for the stabilization of time-delay fuzzy systems. According to the controlled system, the \(H^{\infty }\) 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 problem. A simulation is provided to explore the feasibility of the proposed fuzzy controller design method.

MSC:

93C42 Fuzzy control/observation systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C15 Control/observation systems governed by ordinary differential equations
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