Observer-based fuzzy control design for perturbed fuzzy time-delay systems

In this paper, the nonlinear systems with time-varying delays and parametric uncertainties are represented by an equivalent Takagi-Sugeno type fuzzy model. Based on Convex combination property, Lyapunov criterion, and Razumikhin theorem, some sufficient conditions are derived under which the parallel-distributed fuzzy control can stabilize the whole uncertain fuzzy time-delay systems asymptotically. On the other hand, if the states are not all available, the fuzzy state observers are proposed to estimate all states of the fuzzy systems for fuzzy control. By satisfying some criteria, the stabilization, estimation, and robustness of the fuzzy time-delay systems are also guaranteed. Moreover, if all the time-delays ) (t i τ of the fuzzy systems are the same for all the rules (i.e., τ τ τ = = ) ( ) ( t t j i for all j i ≠ ), we shall propose the simpler and less conservative criteria. The practical example based on the CSTR (continuous stirred tank reactor) model is given to illustrate the control design and its effectiveness. Keywordsfuzzy time-delay system, T-S fuzzy model, parametric uncertainties, fuzzy state observers, Razumikhin theorem.