Boundary Stabilization of a Class of Coupled Hyperbolic‐Parabolic PDE Systems

ABSTRACT This paper considers the boundary state‐feedback stabilization problem of a novel hyperbolic‐parabolic coupled system, which exhibits not only boundary coupling but also complex internal coupling terms. By employing the backstepping method, the original system is transformed into a chosen target system, and two boundary feedback control laws are proposed. Exponential stability in the norm of the target system is established through the construction of an appropriate Lyapunov function. The effectiveness of the controller is demonstrated through a numerical simulation.