Quantum feedback control of linear stochastic systems with feedback-loop time delays

In a quantum feedback control loop, one is often confronted with time delays that mainly originated from the transition delay of signals, which may cause the quantum feedback control system unstable. The purpose of this paper is to deal with a problem of quantum measurement-based feedback control subject to feedback-loop time delays. A quantum version of delay-independent stability criterion as well as an upper bound on a cost function is derived based on quantum Itō rules. We propose one numerical procedure for quantum feedback controller designs, which is then illustrated by an example.