Observer-based output feedback stabilization of an ODE-heat coupled system with non-local term and boundary disturbance via modal decomposition

In this paper, we consider the output feedback stabilization of an ODE-heat coupled system with non-local term and boundary input matched external disturbance. When neglecting the external disturbance, the ODE-heat coupled system with non-local term is stabilized by using modal decomposition method to design a state feedback controller. Applying the active disturbance rejection control (ADRC) approach, the external disturbance is estimated by the extended state observer and canceled in the closed-loop system. Moreover, an infinite-dimensional observer with discontinuous right-hand side is designed to achieve the output feedback control. The well-posedness of the error system is proved by the Galerkin approximation scheme. The asymptotic stability of the closed-loop system is proved by the semigroup method. Numerical simulations are provided to demonstrate the effectiveness of the control design.