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.

中文翻译：

---

相干 $ H ^ {\ infty} $ 相互作用哈密顿量具有不确定性的线性量子系统的控制

这项工作行为健壮 $ H ^ {\ infty} $一类受相互作用哈密顿量微扰的量子系统的分析。提出了这类不确定量子系统的鲁棒严格有界实特性的充要条件。本文着重研究相干鲁棒性$ H ^ {\ infty} $相互作用哈密顿量不确定的量子系统的控制器设计。期望的控制器通过直接和间接耦合与不确定的量子系统连接。提供了在健壮性之间建立连接的必要和充分条件$ H ^ {\ infty} $ 控制问题和规模 $ H ^ {\ infty} $控制问题。提供了一种数值过程以获得相干控制器的系数。给出一个例子来说明控制器的设计方法。