Observer-based fuzzy control of fuzzy time-delay systems with parametric uncertainties

In this paper, non-linear systems with time-varying delays and parametric uncertainties are represented by an equivalent Takagi–Sugeno-type fuzzy model. Based on the 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 τ _i ( t ) of the fuzzy systems are the same for all the rules (i.e. τ _i (t) = τ _j (t) = τ for all i ≠ j), this paper proposes the simpler and less conservative criteria. The practical example based on the continuous stirred tank reactor model and a numerical example are given to illustrate the control design and its effectiveness.