Switching control of semilinear vector reaction-convection-diffusion PDE

This work addresses the stabilization problem for a parabolic system governed by semilinear vector reaction-convection-diffusion equation. We suggest a sampled-data switching control design to stabilize the parabolic system under spatially scheduled actuators. The implementation of controller is either by using one moving actuator that can move to the active subdomain in the negligible time or by N actuators placed in each subdomain. Via Lyapunov-Krasovskii approach, sufficient exponential stability conditions are established in the framework of linear matrix inequalities (LMIs). Simulation example is given to demonstrate the effectiveness of the proposed method.