Coherent $H^{\infty}$ Control for Linear Quantum Systems With Uncertainties in the Interaction Hamiltonian

This work conducts robust $H^{\infty}$ 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 $H^{\infty}$ 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 $H^{\infty}$ control problem and the scaled $H^{\infty}$ control problem. A numerical procedure is provided to obtain coefficients of a coherent controller. An example is presented to illustrate the controller design method.