The problem of controlling the output of a system so as to achieve
asymptotic tracking of prescribed trajectories and/or asymptotic re-
jection of undesired disturbances is a central problem in control the-
ory. A classical setup in which the problem was posed and success- fully
addressed - in the context of linear, time-invariant and finite
dimensional systems - is the one in which the exogenous inputs, namely
commands and disturbances, may range over the set of all possible
trajectories ofa given autonomous linear system, commonly known as the
exogeneous system or, more the exosystem. The case when the exogeneous
system is a harmonic oscillator is, of course, classical. Even in this
special case, the difference between state and error measurement
feedback in the problem ofoutput reg- ulation is profound. To know the
initial condition of the exosystem is to know the amplitude and phase of
the corresponding sinusoid. On the other hand, to solve the output
regulation problem in this case with only error measurement feedback is
to track, or attenu- ate, a sinusoid ofknown frequency but with unknown
amplitude and phase. This is in sharp contrast with alternative
approaches, such as exact output tracking, where in lieu of the
assumption that a signal is within a class of signals generated by an
exogenous system, one instead assumes complete knowledge of the past,
present and future time history of the trajectory to be tracked.