Stability of a Class of Linear Quantum Feedback Systems with Time Delays

The bounded stability problem of linear mixed quantum-classical feedback control systems with time delays is investigated in this paper. The whole feedback system is composed of a quantum plant, a classical controller, and some interconnection devices. Two classes of feedback delays in the feedback loop are considered: constant delays and time-varying delays. The stability of the closed-loop systems under these two classes of time delays is analyzed by constructing different Lyapunov-Krasovskii functions and the corresponding stability criteria are derived, respectively. In particular, a weighting matrix is introduced into stability analysis and the obtained stability results are less conservative than relevant results for this class of quantum systems.