  Continuous feedback control of Langevin processes may be non-Markovian due to
a time lag between the measurement and the control action. We show that this
requires to modify the basic relation between dissipation and time-reversal and
to include a contribution arising from the non-causal character of the reverse
process. We then propose a new definition of the quantity measuring the
irreversibility of a path in a nonequilibrium stationary state, which can be
also regarded as the trajectory-dependent total entropy production. This leads
to an extension of the second law which takes a simple form in the long-time
limit. As an illustration, we apply the general approach to linear systems
which are both analytically tractable and experimentally relevant.
