In this paper, a class of uncertain quantum systems with uncertainties in the interaction Hamiltonian is connected with a coherent controller through direct and indirect couplings. The aim of the paper is to design a robust coherent stability controller to make the closed-loop system robustly mean square stable. A sufficient and necessary condition is presented to build a connection between robust control design with uncertain parameters and scaled control design without uncertain parameters. This condition is also considered for a special class of linear passive quantum systems. A numerical procedure is proposed to obtain explicit expression for parameters of the desired coherent controller using linear matrix inequality, multi-step optimization methods and physical realizability conditions.
This work conducts robust H∞analysis for a class of quantum systems subject to perturbations in the interaction Hamiltonian. A necessary and sufficient condition for the robustly strict bounded real property of this type of uncertain quantum system is proposed. This paper focuses on the study of coherent robust H∞controller design for quantum systems with uncertainties in the interaction Hamiltonian. The desired controller is connected with the uncertain quantum system through direct and indirect couplings. A necessary and sufficient condition is provided to build a connection between the robust H∞control problem and the scaled H∞control problem. A numerical procedure is provided to obtain coefficients of a coherent controller. An example is presented to illustrate the controller design method.
The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems. A general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented. Fundamental properties of stability, dissipation, passivity, and gain for this class of linear quantum models are presented and characterized using complex Lyapunov equations and linear matrix inequalities (LMIs). Coherent
H∞ and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.