This paper utilizes the concept of a transport partial differential equation (PDE) representation of delayed input to solve the classic problem of output feedback control for a common category of uncertain minimum phase linear time-delay systems in spite of co-existence of unknown plant parameter and actuator delay, as well as unmeasurable ordinary differential equation (ODE) and PDE state. In the case of measurable distributed input, the time-varying trajectory tracking is established while in the other case of unmeasurable distributed input, the constant set-point regulation is accomplished. The applicable output feedback control design incorporates the adaptive backstepping technique for ODE plants with the prediction-based boundary control method for PDE systems. There is not any limitation on relative degree of the considered systems. The Lyapunov-based analysis shows the local stability of the closed-loop ODE-PDE cascade systems.