Disturbance rejection in general heterodirectional 1-D linear hyperbolic systems using collocated sensing and control

We solve a disturbance rejection problem for a general class of heterodirectional 1-D linear hyperbolic partial differential equations (PDEs). The disturbance enters at one boundary, while sensing and actuation is limited to the opposite boundary. We do this by combining a separately designed controller and observer into an output feedback controller, and proving stability of the overall closed loop system and exponential regulation of the control objective to zero. The theory is demonstrated in a simulation.