Fuzzy Control for Nonlinear Time-Delay Distributed Parameter Systems under Spatially Point Measurements

This paper introduces a fuzzy control (FC) under spatially point measurements for nonlinear time-delay distributed parameter systems (DPSs) described by parabolic partial differential-difference equations (PDdEs). First, a Takagi-Sugeno (T-S) fuzzy PDdE model is employed to represent the nonlinear time-delay DPSs. Second, with the aid of the T-S fuzzy PDdE model, an FC design under spatially point measurements is developed in the formulation of linear matrix inequalities by constructing an appropriate Lyapunov functional, which can stabilize exponentially the time-delay DPSs. This stabilization condition can be applied to either slowing-varying time delay or fast-varying one. Finally, simulation results of a numerical example are provided to illustrate the effectiveness of the proposed method.