Disturbance Rejection in n + 1 Coupled 1-D Linear Hyperbolic PDEs Using Collocated Sensing and Control

We derive a full state feedback law and a state observer for a class of disturbance rejection problems for n+1 linear coupled partial differential equations (PDEs). The disturbance enters the system at one boundary, while the actuation and sensing are limited to the opposite boundary. We solve this by separately designing a state feedback controller and an observer, and show that they can be combined into an output feedback control law that rejects the effect of the disturbance with exponential decay. The performance of output feedback controller is demonstrated in a simulation.