The equations of quantum feedback control in the regime of good control

We derive the equations of motion describing the feedback control of quantum systemsin the regime of "good control", in which the control is sufficient to keep the systemclose to the desired state. One can view this regime as the quantum equivalent ofthe "linearized" regime for feedback control of classical nonlinear systems. Strikingly,while the dynamics of a single qubit in this regime is indeed linear, that of all largersystems remains nonlinear, in contrast to the classical case. As a first application ofthese equations, we determine the steady-state performance of feedback protocols for asingle qubit that use unbiased measurements.