Robust H∞ control for a class of linear quantum systems with annihilation operators

This paper considers the coherent robust H
^∞
control problem for a class of linear quantum stochastic systems, whose models can be described by the quantum stochastic differential equations in terms of annihilation operators only, where the unknown disturbances from environment and the model uncertainties in the Hamiltonian and coupling operators exist in the system dynamics. We provide a framework to deal with this class of systems, where the robust H
^∞
control problem of the original system is first transformed into that of a scaled system via the quantum bounded real lemma, and then an H
^∞
controller is designed to attenuate the influence of the disturbances on the performance output. In the design of the H
^∞
controller, a pair of algebra Riccati equations are used to obtain a numerical solution of system matrices in the controller. Finally, the simulation experiments on a one-dimensional harmonic oscillator system coupled to three quantum fields verify the effectiveness of the proposed method.