Stabilization of an ODE-PDE cascaded system by boundary control

Abstract Stabilization of an ODE-PDE cascaded system is considered in this paper. The PDE subsystem consists of a system of heat equations, and a control input is set on a boundary. The ODE subsystem is a normal control system cascaded with the PDE subsystem at another boundary, in which its control input is the heat flow rate of the PDE subsystem at this boundary. A boundary control law is constructed by PDE backstepping procedure and lots of complicated mathematical computations. Experiential stability of the closed loop is achieved under this control law.