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arXiv · 2604.06574

Coherent feedback $H^\infty$ control of quantum linear systems

Guofeng Zhang·Ian R. Petersen
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Abstract

The purpose of this paper is to investigate the coherent feedback $H^\infty$ control problem for linear quantum systems. A key contribution is a simplified design methodology that guarantees closed-loop stability and a prescribed level of disturbance attenuation. It is shown that for general linear quantum systems, a physically realizable quantum controller can be obtained by solving at most four Lyapunov equations. In the passive case, a necessary and sufficient condition is provided in terms of two uncoupled pairs of Lyapunov equations. These results represent a significant simplification over the standard approach, which requires solving two coupled algebraic Riccati equations. The effectiveness of the proposed method is demonstrated through two typical quantum optical devices: an empty optical cavity and a degenerate parametric amplifier. These results provide a computationally efficient procedure for the robust and optimal control of quantum optical and optomechanical systems.

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Guofeng Zhang, Ian R. Petersen. 2026-04-08. Coherent feedback $H^\infty$ control of quantum linear systems. https://arxiv.org/abs/2604.06574

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