Coherent robust H∞ control of linear quantum systems with uncertainties in the Hamiltonian and coupling operators

This paper considers a class of uncertain linear quantum systems subject to uncertain perturbations both in the system Hamiltonian and in the coupling operators. A sufficient condition is provided such that these uncertain quantum systems can be guaranteed to be robustly strict bounded real with a given disturbance attenuation parameter. A scaled H∞ problem is shown to have a connection with the stability of the given uncertain quantum system and can be used as an auxiliary system to design a robust H∞ quantum controller. A pair of Riccati equations is used to give explicit formulas for the parameters of a desired controller. Illustrative examples show that for the given uncertain quantum system, the method presented in this paper has improved performance over the existing quantum H∞ control results without considering uncertainties.