Distributed proportional-spatial derivative control design for 3-dimensional parabolic PDE systems

This paper addresses the problem of distributed proportional-spatial derivative (P-sD) control design for a class of linear distributed parameter systems (DPSs) modeled by 3-dimensional parabolic partial differential equations (PDEs). Based on the Lyapunov direct method and the technique of integration by parts, the P-sD control design is developed in terms of standard linear matrix inequality (LMI) such that the closed-loop 3-dimensional PDE system is exponentially stable. Finally, numerical simulation result illustrates its effectiveness.