The Experts below are selected from a list of 279 Experts worldwide ranked by ideXlab platform
Ian R. Petersen - One of the best experts on this subject based on the ideXlab platform.
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a modified frequency Domain Condition for the physical realizability of linear quantum stochastic systems
IEEE Transactions on Automatic Control, 2018Co-Authors: Arash Kh Sichani, Ian R. PetersenAbstract:This paper is concerned with a modified version of the frequency Domain physical realizability (PR) Condition for linear quantum systems. We consider open quantum systems whose dynamic variables satisfy the canonical commutation relations of an open quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to physical quantum systems, these QSDEs must satisfy PR Conditions. We provide a relatively simple proof that the PR Condition is equivalent to the frequency Domain $(J,J)$ -unitarity of the input–output transfer function and orthogonality of the feedthrough matrix of the system without the technical spectral assumptions required in previous work. We also show that the poles and transmission zeros associated with the transfer function of PR linear quantum systems are the mirror reflections of each other about the imaginary axis. An example is provided to illustrate the results.
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A Popov Stability Condition for Uncertain Linear Quantum Systems
arXiv: Quantum Physics, 2013Co-Authors: Matthew R. James, Ian R. Petersen, Valery UgrinovskiiAbstract:This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general class of perturbations to the system Hamiltonian. Then, the special case of a nominal linear quantum system is considered with quadratic perturbations to the system Hamiltonian. In this case, a robust stability Condition is given in terms of a frequency Domain Condition which is of the same form as the standard Popov stability Condition.
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ACC - A Popov stability Condition for uncertain linear quantum systems
2013 American Control Conference, 2013Co-Authors: Matthew R. James, Ian R. Petersen, Valery UgrinovskiiAbstract:This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general class of perturbations to the system Hamiltonian. Then, the special case of a nominal linear quantum system is considered with quadratic perturbations to the system Hamiltonian. In this case, a robust stability Condition is given in terms of a frequency Domain Condition which is of the same form as the standard Popov stability Condition.
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a frequency Domain Condition for the physical realizability of linear quantum systems
IEEE Transactions on Automatic Control, 2012Co-Authors: A J Shaiju, Ian R. PetersenAbstract:A recently emerging approach to the feedback control of linear quantum systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient implementation. An important issue which arises both in the synthesis of linear coherent quantum controllers and in the modeling of linear quantum systems, is the issue of physical realizability. This issue relates to the property of whether a given set of linear quantum stochastic differential equations corresponds to a physical quantum system satisfying the laws of quantum mechanics. Under suitable assumptions, the paper shows that the question of physical realizability is equivalent to a frequency Domain (J,J) -unitary Condition. This is important in controller synthesis since it is the transfer function matrix of the controller which determines the closed loop system behavior.
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Uncertain systems, behaviours and quadratic differential forms
IFAC Proceedings Volumes, 2002Co-Authors: Ian R. Petersen, Jan C. WillemsAbstract:Abstract This paper considers uncertain systems from a behavioural point of view defined via quadratic differential forms. This uncertainty definition is closely related to the integral quadratic constraint uncertainty description commonly found in robust control theory. The paper presents a frequency Domain Condition for the set of behaviours of a given uncertain system to contain the set of behaviours of another given uncertain system. This result is useful in uncertainty modelling problems in which one wishes to consider the trade off between model complexity and model conservatism.
Jürgen Adamy - One of the best experts on this subject based on the ideXlab platform.
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On the Equivalence Between Strict Positive Realness and Strict Passivity of Linear Systems
IEEE Transactions on Automatic Control, 2016Co-Authors: Diego De S. Madeira, Jürgen AdamyAbstract:This technical note presents a proof of the equivalence between the strict passivity of linear time-invariant (LTI) controllable and observable systems and the strict positive realness of their transfer function matrices, where the direct feedthrough $D$ is possibly a non-zero matrix. Although both properties guarantee asymptotic stability, the former is a time Domain Condition and the latter is a frequency Domain concept. A numerical example illustrates our main results.
A J Shaiju - One of the best experts on this subject based on the ideXlab platform.
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a frequency Domain Condition for the physical realizability of linear quantum systems
IEEE Transactions on Automatic Control, 2012Co-Authors: A J Shaiju, Ian R. PetersenAbstract:A recently emerging approach to the feedback control of linear quantum systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient implementation. An important issue which arises both in the synthesis of linear coherent quantum controllers and in the modeling of linear quantum systems, is the issue of physical realizability. This issue relates to the property of whether a given set of linear quantum stochastic differential equations corresponds to a physical quantum system satisfying the laws of quantum mechanics. Under suitable assumptions, the paper shows that the question of physical realizability is equivalent to a frequency Domain (J,J) -unitary Condition. This is important in controller synthesis since it is the transfer function matrix of the controller which determines the closed loop system behavior.
Diego De S. Madeira - One of the best experts on this subject based on the ideXlab platform.
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On the Equivalence Between Strict Positive Realness and Strict Passivity of Linear Systems
IEEE Transactions on Automatic Control, 2016Co-Authors: Diego De S. Madeira, Jürgen AdamyAbstract:This technical note presents a proof of the equivalence between the strict passivity of linear time-invariant (LTI) controllable and observable systems and the strict positive realness of their transfer function matrices, where the direct feedthrough $D$ is possibly a non-zero matrix. Although both properties guarantee asymptotic stability, the former is a time Domain Condition and the latter is a frequency Domain concept. A numerical example illustrates our main results.
A. Megretski - One of the best experts on this subject based on the ideXlab platform.
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Frequency-Domain criteria of robust stability for slowly time-varying systems
IEEE Transactions on Automatic Control, 1995Co-Authors: A. MegretskiAbstract:The problem of stability of feedback systems with structured slowly time-varying uncertain gains is considered. For the case when the pair "uncertain gain/derivative" belongs to a given convex set, a sufficient frequency-Domain Condition of stability is obtained. This Condition is an MIMO generalization of the SISO results derived in the 60s in the context of the positivity theory. >