Coherent H∞Control for a Class of Annihilation Operator Linear Quantum Systems

This paper considers a coherent 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 solution to the control problem can be obtained in terms of a pair of complex algebraic Riccati equations. In addition, the question of physical realizability of the resulting quantum controllers is related to a bounded real property.