Boundary feedback stabilization of an unstable cascaded heat-heat system with different reaction coefficients

The present paper addresses a boundary stabilization problem for a cascaded heat-heat system with different reaction coefficients. A sufficient and necessary condition about two reaction coefficients of the cascaded heat- heat model is found to guarantee the controllability of the coupled system. Based on modal decomposition method, a feedback control is proposed to stabilize the coupled system. Sufficient conditions for exponential stability and well-posedness of the closed-loop systems are derived via the Lyapunov method. The performance is validated by the numerical simulation, which illustrates the efficiency of the proposed control scheme.