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IFAC Proceedings Volumes

Coherent Quantum H∞ Control via a Strict Bounded Real Quantum Controller*

Hendra G. Harrie, Ian R. Petersen

Published Jan 1, 2011• 0 citations
Publisher
DOI
10.3182/20110828-6-it-1002.00185

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This paper considers a coherent Hinfincontrol 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 Hinfincontrol 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.
This paper presents a procedure to synthesize a decentralized coherent robust H∞quantum controller for a class of large-scale uncertain linear complex quantum stochastic systems with a norm-bounded unstructured uncertainty. The H∞control objective is to obtain a strictly bounded real closed loop uncertain quantum system with a specified disturbance attenuation level g > 0. The main idea is that instead of treating the interconnections between quantum subsystems as uncertainties, we consider the neglected off-diagonal blocks of the transfer function matrix of the corresponding non-decentralized quantum controller as additional uncertainties. The resulting decentralized coherent quantum controller is required to satisfy a physical realizability condition.