  The concept of a controlled flow of a dynamical system, especially when the
controlling process feeds information back about the system, is of central
importance in control engineering. In this paper we build on the ideas
presented by Bouten and van Handel (L. Bouten, R. van Handel, "On the
separation principle of quantum control", in Quantum Stochastics and
Information: Statistics, Filtering and Control, World Scientific, 2008) and
develop a general theory of quantum feedback. We elucidate the relationship
between the controlling processes $Z$ and the measured process $Y$, and to this
end make a distinction between what we call the input picture and the output
picture. We should that the input-output relations for the noise fields have
additional terms not present in the standard theory, but that the relationship
between the control processes and measured processes themselves are internally
consistent - we do this for the two main cases of quadrature measurement and
photon-counting measurement. The theory is general enough to include a
modulating filter which processes the measurement readout $Y$ before returning
to the system. This opens up the prospect of applying very general engineering
feedback control techniques to open quantum systems in a systematic manner, and
we consider a number of specific modulating filter problems. Finally, we give a
brief argument as to why most of the rules for making instantaneous feedback
connections (J. Gough, M.R. James, "Quantum Feedback Networks: Hamiltonian
Formulation", Commun. Math. Phys., 287, 1109, 2009) ought to apply for
controlled dynamical networks as well.
