Sampled-data control of an unstable cascaded heat–heat system with different reaction coefficients

The present paper is devoted to sampled-data control design of a PDE–PDE cascade system. These PDEs are governed by heat equations with different reaction coefficients. In order to stabilize the cascaded heat–heat system, we start with the design of continuous-time feedback control law. Then sampled-data control is further proposed for practical reasons. Sufficient conditions are derived for guaranteeing the exponential stability and well-posedness of the corresponding closed-loop system via Lyapunov method and modal decomposition method. Numerical examples illustrate the efficiency of the proposed method.