Quantized State Feedback-Based H∞ Control for Nonlinear Parabolic PDE Systems via Finite-Time Interval

In this paper, the finite-time H∞ control problem of nonlinear parabolic partial differential equation (PDE) systems with parametric uncertainties is studied. Firstly, based on the definition of the quantiser, static state feedback controller and dynamic state feedback controller with quantization are presented, respectively. The finite-time H∞ control design strategies are subsequently proposed to analyze the nonlinear parabolic PDE systems with respect to the effect of quantization. And by constructing appropriate Lyapunov functionals for the studied systems, sufficient conditions for the existence of the feedback control gains and the quantizer’s adjusting parameters which guarantee the prescribed attenuation level of H∞ performance are expressed as nonlinear matrix inequalities. Then, by using some inequalities and decomposition technic, the nonlinear matrix inequalities are transformed to standard linear matrix inequalities (LMIs). Moreover, the optimal H∞ control performances are pursued by solving optimization problems subject to the LMIs. Finally, to illustrate the feasibility and effectiveness of the finite-time H∞ control design strategies, an application to the catalytic rod in a reactor is explored.