Disturbance attenuation of n + 1 coupled hyperbolic PDEs

In this paper, we present a state-feedback and a state-observer for disturbance attenuation problems for a class of n + 1 coupled linear hyperbolic partial differential equations. The disturbance and the sensing are located at the left boundary of the system while the actuation is located at the right boundary of the system (anti-collocated setup). The designs are based on the backstepping method and rely on boundary measurement only. The feedback control law is found by utilizing the fact that the closed-form solution of the equivalent target system can be obtained. Furthermore, by defining a modified L₂-norm, we show the observer is exponentially stable. A numerical example inspired from an oil well drilling problem is presented to validate the results.