Output regulation with bounded energy

The problem of zeroing the output
y = Cx
of the system
\dot{x} = Ax + Bu
by control of the form
u = Fx
under a constraint of the type
\int\min{0}\max{\infty} u'(t)Ru(t) dt < \infty
is solved. The result is used to furnish necessary and sufficient conditions for solvability of the infinite-time optimal linear regulator problem. The control law is shown to be "robust" in the sense of preserving output regulation despite small variations in the feedback gains.