Extended LMI approach to coherent quantum LQG control design

A coherent quantum controller is itself a quantum system that is required to be physically realizable. Thus, additional non-linear and linear constraints must be imposed on the coefficients of a physically realizable quantum controller, which differs the quantum Linear Quadratic Gaussian (LQG) design from the standard LQG problem. The purpose of this paper is to propose one numerical procedure based on extended linear matrix inequality (LMI) approach and new physical realizability conditions proposed in [14] to design a coherent quantum controller. The extended synthesis linear matrix inequalities are, in addition to new analysis tools, less conservative in comparison to the conventional counterparts since the optimization variables related to the system parameters in extended LMIs are independent of the symmetric Lyapunov matrix. These features may be useful in the optimal design of quantum optical networks. For comparison, we apply our numerical procedure to the same example given in [9].