Output feedback stabilization of an ODE-transport cascade system

In this paper, we consider the output feedback stabilization for a cascade system of ODE and transport equation through multiple-point connections. By using an invertible integral transformation, we decouple the connections between ODE and the transport equation, and then design the state feedback to stabilize the whole system. Next, we present an observer to estimate the states of the system, and based on the estimated states, we design an output stabilizing controller. It is shown that the closed-loop system is exponentially stable. The numerical simulation is presented to illustrate the effect of the stabilizing controller.