Sampled-Data Fuzzy Control with Guaranteed Cost for Nonlinear Parabolic PDE Systems via Static Output Feedback

This article introduces a sampled-data (SD) static output feedback fuzzy control (FC) with guaranteed cost for nonlinear parabolic partial differential equation (PDE) systems. First, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is employed to represent the nonlinear PDE system. Second, with the aid of the T-S fuzzy PDE model, a SD FC design with guaranteed cost under spatially averaged measurements is developed in the formulation of linear matrix inequalities by utilizing a time-dependent Lyapunov functional and inequality techniques, which can stabilize exponentially the PDE system while providing an optimized upper bound on the cost function. The membership functions of the proposed controller are determined by the measurement output and independent of the fuzzy PDE plant model. Finally, simulation results are presented to control the diffusion equation and the FitzHugh-Nagumo equation for demonstrating the effectiveness of the proposed method.