Coherent H∞ control for a class of linear complex quantum systems

This paper considers a coherent H^infin 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 H^infin control problem can be obtained in terms of a pair of complex Riccati equations. The paper also considers complex versions of the bounded real lemma, the strict bounded real lemma and the lossless bounded real lemma. For the class of quantum systems under consideration, the question of physical realizability is related to the bounded real and lossless bounded real properties.