Lyapunov-based stabilization mobile control design of linear parabolic PDE systems

This article considers the exponential mobile stabilization control of linear parabolic partial differential equation (PDE) systems. Firstly, a stabilization scheme based on static output feedback (SOF) control and mobile actuator/sensor guidance is proposed. Next, the operator theory is used to discuss the well-posedness of closed-loop PDE systems. Thus, the SOF control and mobile guidance design approach is simultaneously proposed to guarantee that the closed-loop PDE system is exponentially stable. In final, the effectiveness of the design method is verified by numerical simulation.