  We consider the problem of output feedback regulationfor a linear first-order
hyperbolic system with collocatedinput and output in presence of a general
class of disturbancesand noise. The proposed control law is designed through
abackstepping approach incorporating an integral action. Toensure robustness to
delays, the controller only cancels partof the boundary reflection by means of
a tunable parameter.This also enables a trade-off between disturbance and
noisesensitivity.We show that the boundary condition of the obtainedtarget
system can be transformed into a Neutral DifferentialEquation (NDE) and that
this latter system is Input-to-StateStable (ISS). This proves the boundedness
of the controlledoutput for the target system. This extends previous
worksconsidering an integral action for this kind of system [16],
andconstitutes an important step towards practical implementationof such
controllers. Applications and practical considerations,in particular regarding
the system's sensitivity functions arederived in a companion paper.
