  In this paper, we design an output-feedback controller to stabilize n +m
hetero-directional transport partial differential equations (PDEs) coupled on
both domain boundaries to ordinary differential equations (ODEs). This class of
systems can represent, for instance, actuator and load dynamics at the
boundaries of a hyperbolic system. The actuator is located at the connection
point between the PDE and one of the ODEs, and we consider anti-collocated PDE
measurements. We first design a state-observer by combining the backstepping
methodology with time-delay system approaches. We then introduce a state
feedback controller using analogous techniques before designing the wanted
output-feedback control law.
