H∞ control of quantum feedback control systems with time delay

In a quantum feedback control loop, it is often confronted with time delays mainly originated from the transition delay of signals, which may cause quantum feedback control systems unstable. The purpose of this paper is to deal with a problem of quantum measurement-based feedback control systems subject to feedback-loop time delays. A physical model for a quantum measurement-based feedback control system with time delay is presented for the H^∞ control. Fundamental properties such as dissipation, gain and stability for this model are presented and characterized using linear matrix inequalities (LMIs). A numerical procedure is proposed for H^∞ controller designs for our model. An example is given to illustrate our numerical procedure.