Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IFAC-PapersOnLine

Coherent H∞ control for Markovian jump linear quantum systems

Yanan Liu, Daoyi Dong, Ian R. Petersen, Qing Zhong Gao, Steven X. Ding, Hidehiro Yonezawa

Published Jan 1, 2020• 1 citation
Publisher

Abstract

The purpose of this paper is to design a coherent feedback controller for a Markovian jump linear quantum system suffering from a fault signal. The control objective is to bound the effect of the disturbance input on the output for the time-varying quantum system. We prove the relation between the H∞ control problem, the dissipation properties, and the solutions of Riccati differential equations, by which the H∞ controller of the Markovian jump linear quantum system is given by the solutions of Linear Matrix Inequalities (LMIs).

DOI
10.1016/j.ifacol.2020.12.134

Related papers

Fault-tolerant Coherent H-infinity Control for Linear Quantum Systems

Yanan Liu, Daoyi Dong, Ian R. Petersen +4 more

Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this paper is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance and H-infinity disturbance attenuation performance. This paper first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault tolerant H-infinity control problem to the dissipation properties and the solutions of Riccati differential equations, an H-infinity controller for the quantum system is then designed by solving a set of linear matrix inequalities (LMIs). In particular, an algorithm is employed to introduce additional noises and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. For real applications of the developed fault-tolerant control strategy, we present a linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values. It is demonstrated that a quantum H-infinity controller can be designed and implemented using some basic optical components to achieve the desired control goal.

arXiv:2003.09609•Mar 21, 2020•1 citation

Fault-Tolerant Coherent $H^\infty$ Control for Linear Quantum Systems

Yanan Liu, Daoyi Dong, Ian R. Petersen +4 more

Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this article is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance and$H^\infty$disturbance attenuation performance. This article first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault-tolerant$H^\infty$control problem to the dissipation properties and the solutions of Riccati differential equations, an$H^\infty$controller for the quantum system is then designed by solving a set of linear matrix inequalities. In particular, an algorithm is employed to introduce additional quantum inputs and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. Also, we propose a real application of the developed fault-tolerant control strategy to quantum optical systems. A linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values due to the fault processes, can be modeled as a linear Markovian jumping system. It is demonstrated that a quantum$H^\infty$controller can be designed and implemented using some basic optical components to achieve the desired control goal for this class of systems.

IEEE Transactions on Automatic Control•Sep 28, 2021•17 citations

H∞ control of quantum feedback control systems with time delay

Shi Wang, M. R. James

In a quantum feedback control loop, it is often confronted with time delays mainly originated from the transition delay of signals, which may cause quantum feedback control systems unstable. The purpose of this paper is to deal with a problem of quantum measurement-based feedback control systems subject to feedback-loop time delays. A physical model for a quantum measurement-based feedback control system with time delay is presented for the H∞control. Fundamental properties such as dissipation, gain and stability for this model are presented and characterized using linear matrix inequalities (LMIs). A numerical procedure is proposed for H∞controller designs for our model. An example is given to illustrate our numerical procedure.

Asian Control Conference (ASCC)•May 1, 2015•2 citations

Robust H∞ control for a class of linear quantum systems with annihilation operators

Xiujuan Lu, Sen Kuang

This paper considers the coherent robust H∞control problem for a class of linear quantum stochastic systems, whose models can be described by the quantum stochastic differential equations in terms of annihilation operators only, where the unknown disturbances from environment and the model uncertainties in the Hamiltonian and coupling operators exist in the system dynamics. We provide a framework to deal with this class of systems, where the robust H∞control problem of the original system is first transformed into that of a scaled system via the quantum bounded real lemma, and then an H∞controller is designed to attenuate the influence of the disturbances on the performance output. In the design of the H∞controller, a pair of algebra Riccati equations are used to obtain a numerical solution of system matrices in the controller. Finally, the simulation experiments on a one-dimensional harmonic oscillator system coupled to three quantum fields verify the effectiveness of the proposed method.

Youth Academic Annual Conference of Chinese Association of Automation (YAC)•May 1, 2018•0 citations

Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems

Guofeng Zhang, M. R. James

The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems. A general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented. Fundamental properties of stability, dissipation, passivity, and gain for this class of linear quantum models are presented and characterized using complex Lyapunov equations and linear matrix inequalities (LMIs). Coherent H∞and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.

arXiv:1010.4369•IEEE Transactions on Automatic Control•Dec 10, 2010•123 citations

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

Guofeng Zhang, Ian R. Petersen

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.

quant-pharXiv:2604.06574•Apr 9, 2026•0 citations
The purpose of this paper is to design a coherent feedback controller for a Markovian jump linear quantum system suffering from a fault signal. The control objective is to bound the effect of the disturbance input on the output for the time-varying quantum system. We prove the relation between the H∞ control problem, the dissipation properties, and the solutions of Riccati differential equations, by which the H∞ controller of the Markovian jump linear quantum system is given by the solutions of Linear Matrix Inequalities (LMIs).
Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this paper is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance and H-infinity disturbance attenuation performance. This paper first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault tolerant H-infinity control problem to the dissipation properties and the solutions of Riccati differential equations, an H-infinity controller for the quantum system is then designed by solving a set of linear matrix inequalities (LMIs). In particular, an algorithm is employed to introduce additional noises and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. For real applications of the developed fault-tolerant control strategy, we present a linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values. It is demonstrated that a quantum H-infinity controller can be designed and implemented using some basic optical components to achieve the desired control goal.
Fault-Tolerant Coherent H∞H^\inftyH∞ Control for Linear Quantum Systems
Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this article is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance andH∞H^\inftyH∞disturbance attenuation performance. This article first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault-tolerantH∞H^\inftyH∞control problem to the dissipation properties and the solutions of Riccati differential equations, anH∞H^\inftyH∞controller for the quantum system is then designed by solving a set of linear matrix inequalities. In particular, an algorithm is employed to introduce additional quantum inputs and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. Also, we propose a real application of the developed fault-tolerant control strategy to quantum optical systems. A linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values due to the fault processes, can be modeled as a linear Markovian jumping system. It is demonstrated that a quantumH∞H^\inftyH∞controller can be designed and implemented using some basic optical components to achieve the desired control goal for this class of systems.
In a quantum feedback control loop, it is often confronted with time delays mainly originated from the transition delay of signals, which may cause quantum feedback control systems unstable. The purpose of this paper is to deal with a problem of quantum measurement-based feedback control systems subject to feedback-loop time delays. A physical model for a quantum measurement-based feedback control system with time delay is presented for the H∞control. Fundamental properties such as dissipation, gain and stability for this model are presented and characterized using linear matrix inequalities (LMIs). A numerical procedure is proposed for H∞controller designs for our model. An example is given to illustrate our numerical procedure.
This paper considers the coherent robust H∞control problem for a class of linear quantum stochastic systems, whose models can be described by the quantum stochastic differential equations in terms of annihilation operators only, where the unknown disturbances from environment and the model uncertainties in the Hamiltonian and coupling operators exist in the system dynamics. We provide a framework to deal with this class of systems, where the robust H∞control problem of the original system is first transformed into that of a scaled system via the quantum bounded real lemma, and then an H∞controller is designed to attenuate the influence of the disturbances on the performance output. In the design of the H∞controller, a pair of algebra Riccati equations are used to obtain a numerical solution of system matrices in the controller. Finally, the simulation experiments on a one-dimensional harmonic oscillator system coupled to three quantum fields verify the effectiveness of the proposed method.
The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems. A general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented. Fundamental properties of stability, dissipation, passivity, and gain for this class of linear quantum models are presented and characterized using complex Lyapunov equations and linear matrix inequalities (LMIs). Coherent H∞and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.
Coherent feedback H∞H^\inftyH∞ control of quantum linear systems
The purpose of this paper is to investigate the coherent feedback H∞H^\inftyH∞ 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.