Coherent quantum H^∞ control via a strict bounded real quantum controller

We present a systematic method to synthesize a coherent quantum robust H1 controller for a class of linear complex quantum stochastic systems, which is defined only in terms of annihilation operators, with norm-bounded structured uncertainties. This controller is required to be stable and strict bounded real in order to be physically realizable. The main idea of our approach is to introduce an additional uncertainty to form an artificial uncertain quantum system used to design the desired quantum controller. The H^∞ control objective is to achieve a strict bounded real closed loop quantum system with a specified disturbance attenuation level. The solution to this control problem is given in terms of stabilizing solutions to the parameterized complex Riccati equations.