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IEEE Conference on Decision and Control (CDC)

H∞ Control of Linear Quantum Systems

M. R. James, Ian R. Petersen

Published Dec 1, 2006• 4 citations
Publisher

Abstract

The purpose of this paper is to formulate and solve a H∞controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology. A quantum version of the strict bounded real lemma is presented and from this, a quantum version of the two Riccati solution to the H∞control problem is derived

DOI
10.1109/cdc.2006.377445

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The purpose of this paper is to formulate and solve a H∞controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology. A quantum version of the strict bounded real lemma is presented and from this, a quantum version of the two Riccati solution to the H∞control problem is derived
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H∞H^{\infty}H∞ Control of Linear Quantum Stochastic Systems
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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.