Robust H~? Control And Time-Delay Stability For Linear Quantum Feedback Systems

With the development and applications of quantum information technology,quan-tum control has been attracting wide reseach interests.Research on linear quan-tum stochastic systems,which widely exist in the fields of quantum optics and opto-mechanical systems has significantly promoted the development of quantum control.In a real environment,any quantum system is inevitably disturbed by external factors and therefore some uncertainties will be introduced to the system,e.g.,model uncer-tainties,unknown disturbance signals,and time delays,which will cause the deviations or erros in the controller design and performance analysis.The controller design and stability analysis for these uncertain systems play a significant role in the devel opment of quantum technology.Against this background,the robust H? method will be used to design the coherent controller for a class of linear quantum passive systems with model uncertainties,and based on the Lyapunov-Krasovskii function,the stability conditions for a class of linear quantum feedback systems with time delays will be analyzed in this paper.The main contents are as follows:(I)A brief review of the development history of quantum feedback control is given,and the research status of robust H00 control and time-dealy stability in in quantum field is introduced in detail.On this basis,the research contents are introduced.(2)Robust H? control for linear quantum passive systems with model uncertain-ties.For a class of linear quantum passive systems with model uncertainties,the H?method is used to design a coherent controller with the good robustness,which can re-strict the impact of disturbance signals on the system performance output within a preset scope.At first,the model uncertainties in qunatum plant can be denoted as the uncer-tainties in the Hamiltonian,the coupling operator,and the scattering matrix,which can guarantee the physical realizability of plant described by quantum stochastic differential equations.Then,based on the quantum bounded real lemma of the complex field,the robust H? controller design of the original uncertain plant is transformed to the con-troller design of a new scaled system.Further,the later is transformed to the solving problem of a couple of Riccati equation.Finally,numerical simulations on an optical system coupled to three optical channels are performed to verify the effectiveness of the proposed method.(3)Stability analysis for a class of linear quantum feedback systems with time delays.The stability problem for measurement-based feedback control systems is in-vestigated when the closed loop exists the transition delay of signals.Firstly,the defini-tion of quantum bounded stability is introduced.Next,for constant delay,two different Lyapunov-Krasovskii functions are designed,and based on quantum Ito rules,two types of stability conditions with different conservatism are derived.Further,a stability cri-teria for a special class of time-varying delays is also proposed.(4)The main results in this paper are summarized,and the future reseach is prospected,focusing on the unsolved problems in this paper.