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We consider the problem of output feedback regulationfor a linear first-orderhyperbolic system with collocatedinput and output in presence of a generalclass of disturbancesand noise. The proposed control law is designed throughabackstepping approach incorporating an integral action. Toensure robustness todelays, the controller only cancels partof the boundary reflection by means ofa tunable parameter.This also enables a trade-off between disturbance andnoisesensitivity.We show that the boundary condition of the obtainedtargetsystem can be transformed into a Neutral DifferentialEquation (NDE) and thatthis latter system is Input-to-StateStable (ISS). This proves the boundednessof the controlledoutput for the target system. This extends previousworksconsidering an integral action for this kind of system [16],andconstitutes an important step towards practical implementationof suchcontrollers. Applications and practical considerations,in particular regardingthe system's sensitivity functions arederived in a companion paper.

Robust output regulation of 2 x 2 hyperbolic systems part I: Control law and Input-to-State Stability