Observer-based stabilization of an unstable ODE-heat cascade system with multiple-point connection

In this paper, we consider the output feedback stabilization for a cascade of ODE-heat system through multiple-point connection, where the point outputs of the heat are flowing into the ODE, and the control is proposed on the ODE and the boundary of the heat simultaneously. An observer system is presented to estimate the ODE and the heat variables, and the error system is showed to be exponentially convergent. Based on the estimated variables, an output feedback control is designed using two invertible transformations to exponentially stabilize the entire system. Some numerical simulation results are presented to validate the theoretical conclusions.