Coherent LQG control for a class of linear complex quantum systems

This paper considers a coherent LQG control problem for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. For this class of quantum systems, a method for designing an LQG controller which satisfies a physical realizability condition is developed. This result is related to a recent result on constructing strictly positive real LQG controllers. The main idea of the paper involves constructing a suitable cost function for the LQG problem such that a physically realizable controller is obtained. The resulting controller provides robust stability as well as optimal performance.