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This paper is concerned with networks of identical linear quantum stochastic systems which interact with each other and external bosonic fields in a translation invariant fashion. The systems are associated with sites of a multidimensional lattice and are governed by coupled linear quantum stochastic differential equations (QSDEs). The block Toeplitz coefficients of these QSDEs are specified by the energy and coupling matrices which quantify the Hamiltonian and coupling operators for the component systems. We discuss the invariant Gaussian quantum state of the network when it satisfies a stability condition and is driven by statistically independent vacuum fields. A quadratic-exponential functional (QEF) is considered as a risk-sensitive performance criterion for a finite fragment of the network over a bounded time interval. This functional involves a quadratic function of dynamic variables of the component systems with a block Toeplitz weighting matrix. Assuming the invariant state, we study the spatio-temporal asymptotic rate of the QEF per unit time and per lattice site in the thermodynamic limit of unboundedly growing time horizons and fragments of the lattice. A spatio-temporal frequency-domain formula is obtained for the QEF rate in terms of two spectral functions associated with the real and imaginary parts of the invariant quantum covariance kernel of the network variables. A homotopy method and asymptotic expansions for evaluating the QEF rate are also discussed. [ABSTRACT FROM AUTHOR]

This paper is concerned with quantum harmonic oscillators consisting of a quantum plant and a directly coupled coherent quantum observer. We employ discounted quadratic performance criteria in the form of exponentially weighted time averages of the second-order moments of the system variables. Small-gain-theorem bounds are obtained for the back-action of the observer on the covariance dynamics of the plant in terms of the plant–observer coupling. A coherent quantum filtering (CQF) problem is formulated as the minimization of the discounted mean square of an estimation error, with which the dynamic variables of the observer approximate those of the plant. The cost functional also involves a quadratic penalty on the plant–observer coupling matrix in order to mitigate the back-action effect. For the discounted mean square optimal CQF problem with penalized back-action, we establish the first-order necessary conditions of optimality in the form of algebraic matrix equations. By using the Hamiltonian structure of the Heisenberg dynamics and Lie-algebraic techniques, this set of equations is represented in a more explicit form for equally dimensioned plant and observer. For a class of such observers with autonomous estimation error dynamics, we obtain a solution of the CQF problem and outline a homotopy method. The computation of the performance criteria and the observer synthesis are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

The development of estimation and control theories for quantum systems is a fundamental task for practical quantum technology. This vision article presents a brief introduction to challenging problems and potential opportunities in the emerging areas of quantum estimation, control and learning. The topics cover quantum state estimation, quantum parameter identification, quantum filtering, quantum open-loop control, quantum feedback control, machine learning for estimation and control of quantum systems, and quantum machine learning. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices pertaining to finite-level systems. The system interacts with external bosonic fields, and its Hamiltonian and coupling operators depend linearly on the system variables. This results in a Hudson--Parthasarathy quantum stochastic differential equation (QSDE) whose drift and dispersion terms are affine and linear functions of the system variables. The quasilinearity of the QSDE leads to tractable dynamics of mean values and higher-order multipoint moments of the system variables driven by vacuum input fields. This allows for the closed-form computation of the quasi-characteristic function of the invariant quantum state of the system and infinite-horizon asymptotic growth rates for a class of cost functionals. The tractability of the moment dynamics is also used for mean square optimal Luenberger observer design in a measurement-based filtering problem for a quasilinear quantum plant, which leads to a Kalman-like quantum filter. [ABSTRACT FROM AUTHOR]

This paper is concerned with exponential moments of integral-of-quadratic functions of quantum processes with canonical commutation relations of position-momentum type. Such quadratic-exponential functionals (QEFs) arise as robust performance criteria in control problems for open quantum harmonic oscillators (OQHOs) driven by bosonic fields. We develop a randomised representation for the QEF using a Karhunen–Loeve expansion of the quantum process on a bounded time interval over the eigenbasis of its two-point commutator kernel, with noncommuting position-momentum pairs as coefficients. This representation holds regardless of a particular quantum state and employs averaging over an auxiliary classical Gaussian random process whose covariance operator is specified by the commutator kernel. This allows the QEF to be related to the moment-generating functional of the quantum process and computed for multipoint Gaussian states. For stationary Gaussian quantum processes, we establish a frequency-domain formula for the QEF rate in terms of the Fourier transform of the quantum covariance kernel in composition with trigonometric functions. A differential equation is obtained for the QEF rate with respect to the risk sensitivity parameter for its approximation and numerical computation. The QEF is also applied to large deviations and worst-case mean square cost bounds for OQHOs in the presence of statistical uncertainty with a quantum relative entropy description. [ABSTRACT FROM AUTHOR]

This paper is concerned with risk-sensitive performance analysis for linear quantum stochastic systems interacting with external bosonic fields. We consider a cost functional in the form of the exponential moment of the integral of a quadratic polynomial of the system variables over a bounded time interval. Such functionals are related to more conservative behaviour and robustness of systems with respect to statistical uncertainty, which makes the challenging problems of their computation and minimization practically important. To this end, we obtain an integro-differential equation for the time evolution of the quadratic–exponential functional, which is different from the original quantum risk-sensitive performance criterion employed previously for measurement-based quantum control and filtering problems. Using multi-point Gaussian quantum states for the past history of the system variables and their first four moments, we discuss a quartic approximation of the cost functional and its infinite-horizon asymptotic behaviour. The computation of the asymptotic growth rate of this approximation is reduced to solving two algebraic Lyapunov equations. Further approximations of the cost functional, based on higher-order cumulants and their growth rates, are applied to large deviations estimates in the form of upper bounds for tail distributions. We discuss an auxiliary classical Gaussian–Markov diffusion process in a complex Euclidean space which reproduces the quantum system variables at the level of covariances but has different fourth-order cumulants, thus showing that the risk-sensitive criteria are not reducible to quadratic–exponential moments of classical Gaussian processes. The results of the paper are illustrated by a numerical example and may find applications to coherent quantum risk-sensitive control problems, where the plant and controller form a fully quantum closed-loop system, and other settings with nonquadratic cost functionals. [ABSTRACT FROM AUTHOR]

This paper combines probabilistic and algebraic techniques for computing quantum expectations of operator exponentials (and their products) of quadratic forms of quantum variables in Gaussian states. Such quadratic-exponential functionals (QEFs) resemble quantum statistical mechanical partition functions with quadratic Hamiltonians and are also used as performance criteria in quantum risk-sensitive filtering and control problems for linear quantum stochastic systems. We employ a Lie-algebraic correspondence between complex symplectic matrices and quadratic-exponential functions of system variables of a quantum harmonic oscillator. The complex symplectic factorizations are used together with a parametric randomization of the quasi-characteristic or moment-generating functions according to an auxiliary classical Gaussian distribution. This reduces the QEF to an exponential moment of a quadratic form of classical Gaussian random variables with a complex symmetric matrix and is applicable to recursive computation of such moments. [ABSTRACT FROM AUTHOR]

Among first order optimization methods, Polyak's heavy ball method has long been known to guarantee the asymptotic rate of convergence matching Nesterov's lower bound for functions defined in an infinite-dimensional space. In this paper, we use results on the robust gain margin of linear uncertain feedback control systems to show that the heavy ball method is provably worst-case asymptotically optimal when applied to quadratic functions in a finite dimensional space. [ABSTRACT FROM AUTHOR]

This paper provides a state feedback stabilization approach for nonlinear systems of relative degree less than or equal to two by rendering them nonlinear negative imaginary (NI) systems. Conditions are provided under which a nonlinear system can be made a nonlinear NI system or a nonlinear output strictly negative imaginary (OSNI) system. Roughly speaking, an input-affine nonlinear system can be rendered nonlinear NI and nonlinear OSNI if it has a normal form with relative degree less than or equal to two after possible output transformation. In addition, if the internal dynamics of the normal form are input-to-state stable, then there exists a state feedback input that stabilizes the system. This stabilization result is then extended to achieve stability for systems with a nonlinear NI uncertainty. A numerical example is provided to illustrate the process of stabilizing an uncertain system using the proposed results. [ABSTRACT FROM AUTHOR]

This paper is concerned with multimode open quantum harmonic oscillators (OQHOs) described by linear quantum stochastic differential equations with multichannel external bosonic fields. We consider the exponentially fast decay in the two-point commutator matrix of the system variables as a manifestation of quantum decoherence. Such dissipative effects are caused by the interaction of the system with its environment and lead to a loss of specific features of the unitary evolution which the system would have in the case of isolated dynamics. These features provide nonclassical resources exploited in quantum computation and quantum information processing technologies. We discuss a system-theoretic definition of decoherence time in terms of the commutator matrix decay and obtain an upper bound for it using algebraic Lyapunov inequalities. Employing spectrum perturbation techniques, we investigate the asymptotic behaviour of a related Lyapunov exponent for the oscillator when the system-field coupling is specified by a small coupling strength parameter and a given coupling shape matrix. The invariant quantum state of the system, driven by vacuum fields, in the weak-coupling limit is also studied. We illustrate the results for one- and two-mode oscillators with multichannel external fields and outline their application to a decoherence control problem for a feedback interconnection of multimode OQHOs. [ABSTRACT FROM AUTHOR]

This paper is concerned with the generation of Gaussian invariant states in cascades of open quantum harmonic oscillators governed by linear quantum stochastic differential equations. We carry out infinitesimal perturbation analysis of the covariance matrix for the invariant Gaussian state of such a system and the related purity functional subject to inaccuracies in the energy and coupling matrices of the subsystems. This leads to the problem of balancing the state-space realizations of the component oscillators through symplectic similarity transformations in order to minimize the mean square sensitivity of the purity functional to small random perturbations of the parameters. This results in a quadratic optimization problem with an effective solution in the case of cascaded one-mode oscillators, which is demonstrated by a numerical example. The findings of the paper are applicable to robust state generation in quantum stochastic networks. [ABSTRACT FROM AUTHOR]

A number of recent works employ bilinear Hamiltonian interactions between Linear Quantum Stochastic Systems (LQSSs). To the authors’ knowledge, implementation schemes for such interactions exist only between single-mode systems. In this work, we propose a general method for the implementation of an arbitrary bilinear Hamiltonian interaction between two multi-mode LQSSs via a feedback interconnection. As an application, we show that the direct interaction realization of a certain coherent quantum control architecture is very useful for design and optimization. [ABSTRACT FROM AUTHOR]

This paper is concerned with a linear fractional representation approach to the synthesis of linear coherent quantum controllers for a given linear quantum plant. The plant and controller represent open quantum harmonic oscillators and are modelled by linear quantum stochastic differential equations. The feedback interconnections between the plant and the controller are assumed to be established through quantum bosonic fields. In this framework, conditions for the stabilization of a given linear quantum plant via linear coherent quantum feedback are addressed using a stable factorization approach. The class of all stabilizing quantum controllers is parameterized in the frequency domain. Coherent quantum weighted ℋ 2 and ℋ ∞ control problems for linear quantum systems are formulated in the frequency domain. Finally, a projected gradient descent scheme is outlined for the coherent quantum weighted ℋ 2 control problem. [ABSTRACT FROM AUTHOR]

This paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a finite horizon H ∞ control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of sampled-data measurements. The methodology adopted involves an equivalence between the quantum problem and two auxiliary classical problems. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We study a coherent-classical estimation scheme for a class of linear quantum systems, where the estimator is a mixed quantum–classical system that may or may not involve coherent feedback. We show that when the quantum plant or the quantum part of the estimator (coherent controller) is an annihilation operator only system, coherent-classical estimation without coherent feedback can provide no improvement over purely-classical estimation. Otherwise, coherent-classical estimation without feedback can be better than classical-only estimation for certain homodyne detector angles, although the former is inferior to the latter for the best choice of homodyne detector angle. Moreover, we show that coherent-classical estimation with coherent feedback is no better than classical-only estimation, when both the plant and the coherent controller are annihilation operator only systems. Otherwise, coherent-classical estimation with coherent feedback can be superior to purely-classical estimation, and in this case, the former is better than the latter for the optimal choice of homodyne detector angle. [ABSTRACT FROM AUTHOR]

This paper considers a class of uncertain linear quantum systems subject to uncertain perturbations both in the system Hamiltonian and in the coupling operators. A sufficient condition is provided such that these uncertain quantum systems can be guaranteed to be robustly strict bounded real with a given disturbance attenuation parameter. A scaled H ∞ problem is shown to have a connection with the stability of the given uncertain quantum system and can be used as an auxiliary system to design a robust H ∞ quantum controller. A pair of Riccati equations is used to give explicit formulas for the parameters of a desired controller. Illustrative examples show that for the given uncertain quantum system, the method presented in this paper has improved performance over the existing quantum H ∞ control results without considering uncertainties. [ABSTRACT FROM AUTHOR]

Given any covariance matrix corresponding to a so-called pure Gaussian state, a linear quantum system can be designed to achieve the assigned covariance matrix. In most cases, however, one might obtain a system that is difficult to realize in practice. In this paper, we restrict our attention to a special class of linear quantum systems, i.e., systems with diagonal passive Hamiltonian and a single dissipative channel. The practical implementation of such a system would be relatively simple. We then parametrize the class of pure Gaussian state covariance matrices that can be achieved by this particular type of linear quantum system. [ABSTRACT FROM AUTHOR]

We consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust H ∞ estimation for uncertain linear quantum systems. The estimation problem is solved by converting it to a suitably scaled H ∞ control problem. The solution is obtained in the form of two algebraic Riccati equations. Relevant examples involving dynamic squeezers are presented to illustrate the efficacy of our method. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this note, an improved method of ultimate bound computation for a linear switched system under arbitrary switching is presented. An ultimate bound for a linear switched system can be computed by solving a class of linear matrix inequalities. The effectiveness of the obtained results is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

The negative imaginary (NI) property occurs in many important applications. For instance, flexible structure systems with collocated force actuators and position sensors can be modelled as negative imaginary systems. In this study, a data‐driven controller synthesis methodology for NI systems is presented. In this approach, measured frequency response data of the plant is used to construct the controller frequency response at every frequency by minimising a cost function. Then, this controller response is used to identify the controller transfer function using system identification methods. [ABSTRACT FROM AUTHOR]

This paper presents a survey of some of the main results in the theory of negative imaginary systems. The paper also presents some applications of negative imaginary systems theory in the design of robust controllers. In particular, the paper concentrates on the application of negative imaginary systems theory in the area of control of atomic force microscopes. [ABSTRACT FROM AUTHOR]

This paper presents a scheme for the design of a robust fixed-lag smoother for a class of nonlinear uncertain systems. The proposed approach combines a nonlinear robust estimator with a stable fixed-lag smoother, to improve the estimation error covariance. The robust fixed-lag smoother is based on the use of integral quadratic constraints and minimax linear quadratic regulator estimation and control theory. The state estimator uses a copy of the system nonlinearity in the estimator and combines an approximate model of the delayed states to produce a smoother signal. Also in this work, a characterization of the delay approximation error is presented, and the corresponding integral quadratic constraint is included in the design, which gives a guaranteed bound on the performance cost function. In order to see the effectiveness of the method, it is applied to a quantum optical phase estimation problem. Results show a significant improvement in the error covariance of the estimator when compared with a robust nonlinear filter. [ABSTRACT FROM AUTHOR]

A new method is given to estimate an ultimate state bound on a time-varying linear system with delay and bounded disturbances by using some results on Metzler matrices. The effectiveness of the obtained results is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

This paper considers a class of uncertain quantum systems subject to non-quadratic perturbations in the system Hamiltonian. Results on performance analysis for this class of systems are presented using a linear matrix inequality method. Guaranteed cost coherent controllers are designed through adding a controller Hamiltonian to the quantum systems. A numerical procedure is proposed for the controller synthesis to deal with a non-convex problem in the design process. An example of a quantum system comprised of a Josephson junction coupled to an electromagnetic resonant cavity is presented to illustrate the control method. [ABSTRACT FROM AUTHOR]

This paper is concerned with dissipativity theory and robust performance analysis and design of discrete-time stochastic systems driven by statistically uncertain random noise. The uncertainty is quantified by the conditional relative entropy of the actual probability law of the noise with respect to a nominal product measure corresponding to a white noise sequence. We discuss a balance equation, dissipation inequality, and superadditivity property for the corresponding conditional relative entropy supply as a function of time. The problem of minimizing the supply, required to drive the system between given state distributions over a specified time horizon, is considered. Such variational problems, involving entropy and probabilistic boundary conditions, are known in the literature as Schrödinger bridge problems. In application to control systems, the minimum required conditional relative entropy supply characterizes the robustness of the system with respect to a statistically uncertain random noise. We obtain a dynamic programming Bellman equation for the minimum required supply and establish a Markov property of the worst-case noise with respect to the state of the system. For multivariable linear systems with a Gaussian white noise sequence as the nominal noise model and Gaussian initial and terminal state distributions, the minimum required conditional relative entropy supply is obtained using an algebraic Riccati equation which admits a closed-form solution. We propose a computable robustness index for such systems subjected to statistically uncertain random noises whose relative entropy rate does not exceed a given threshold, and provide examples to illustrate this approach. We also consider a minimax problem of robust optimization of systems against the class of noises and demonstrate its solution for a robust filter design example. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a survey of the most significant results on robust control theory. In particular, we study the modeling of uncertain systems, robust stability analysis for systems with unstructured uncertainty, robustness analysis for systems with structured uncertainty, and robust control system design including control methods. The paper also presents some more recent results on deterministic and probabilistic methods for systems with uncertainty. [Copyright &y& Elsevier]

In this paper, a finite horizon H∞ control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of delayed measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, the finite horizon H∞ control problem for the class of linear quantum systems under consideration is solved for the case of delayed measurements by solving the finite horizon H∞ control problem for an equivalent stochastic H∞ control problem following a dynamic game approach. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents a new method to synthesize a decentralized state feedback robust H ∞ controller for a class of large-scale linear uncertain systems satisfying integral quadratic constraints. The decentralized controller is constructed by taking only block-diagonal elements of a nondecentralized state feedback controller and treating neglected off-diagonal blocks as uncertainties. A solution to this controller synthesis problem is given in terms of a stabilizing solution to a parametrized algebraic Riccati equation where the parameters are obtained using a differential evolution algorithm.Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents a new method to construct a decentralized nonlinear robust H ∞ controller for a class of large-scale nonlinear uncertain systems. The admissible uncertainties and nonlinearities in the system satisfy integral quadratic constraints and global Lipschitz conditions, respectively. The decentralized controller, which is required to be stable, is capable of exploiting known nonlinearities and interconnections between subsystems without treating them as uncertainties. Instead, additional uncertainties are introduced because of the discrepancies between nondecentralized and decentralized nonlinear output feedback controllers. The H ∞ control objective is to achieve an absolutely stable closed-loop system with a specified disturbance attenuation level. A solution to this control problem involves stabilizing solutions to algebraic Riccati equations parametrized by scaling constants corresponding to the uncertainties and nonlinearities. This formulation is nonconvex; hence, an evolutionary optimization method is applied to solve the control problem considered. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents an approach to discrete-time robust H∞ control for a class of nonlinear uncertain systems on the basis of the use of Sum Quadratic Constraints. The approach involves controllers, which include copies of the system nonlinearities in the controller. The nonlinearities being considered are those that satisfy a certain global Lipschitz condition. The linear part of the controller is synthesized using linear robust H∞ control theory, and this leads to a nonlinear controller, which gives an upper bound on the attainable disturbance attenuation level. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the structure of uncertain linear systems building on concepts of robust unobservability and possible controllability. The paper presents a new geometric characterization of the possibly controllable states. When combined with previous geometric results on robust unobservability, the results of this paper lead to a general Kalman type decomposition for uncertain linear systems which can be applied to the problem of obtaining reduced order uncertain system models. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the coherent quantum linear quadratic Gaussian (LQG) control problem of constructing an optimal controller for linear quantum plants using a quadratic performance criterion. Coherent quantum feedback control does not employ classical measurements which inherently entail the loss of quantum information. A coherent quantum controller is itself a quantum system and this imposes physical realizability (PR) constraints on the quantum stochastic differential equation which governs such a controller. PR corresponds to the equivalence of the controller to an open quantum harmonic oscillator whereby its state-space matrices are related to the Hamiltonian and coupling operators of the oscillator. The Hamiltonian parameterization of the controller is combined with Frechet differentiation of the LQG cost with respect to the state-space matrices in order to obtain equations for the optimal controller. A quasi-separation property for the gain matrices of the quantum controller is established, and a Newton-like iterative scheme for the numerical solution of the equations is outlined. [Copyright &y& Elsevier]

Abstract: In [Dong, D. and Petersen, I.R. (2012). Sliding mode control of two-level quantum systems. Automatica, 48, 725–735], a sliding mode control approach has been proposed for two-level quantum systems to deal with bounded uncertainties in the system Hamiltonian. This paper further extends these results in two directions. One extension is to consider the effect of uncertainties during the process of driving the system’s state back to the sliding mode domain from outside and we propose two approaches to accomplish this control task. The other extension generalizes the previous design approach to consider uncertainties described as perturbations in the free Hamiltonian. [Copyright &y& Elsevier]

Abstract: This paper addresses the Lagrange stability analysis problem and the state feedback Lagrange stabilization problem for pendulum-like systems with multiple nonlinearities. An existing method for analysing the Lagrange stability of pendulum-like systems with a single nonlinearity is generalized to pendulum-like systems with multiple nonlinearities. Also, a non-degeneracy condition of the existing Lagrange stability criterion is removed and a strict frequency-domain inequality is used instead. To study the state feedback Lagrange stabilization problem, this paper develops an extended strict bounded real lemma for linear systems which are not stable but stabilizable. A sufficient condition for state feedback Lagrange stabilization is proposed in terms of an algebraic Riccati equation with a sign indefinite solution. [Copyright &y& Elsevier]

Abstract: The paper is concerned with the notion of lossless negative imaginary systems and their stabilization using strictly negative imaginary controllers through positive feedback. Firstly, the concept of lossless negative imaginary transfer functions is introduced and some properties of such transfer functions are studied. Secondly, a Lossless Negative Imaginary Lemma is given which establishes conditions on matrices appearing in a minimal state-space realization that are necessary and sufficient for a transfer function to be lossless negative imaginary. Thirdly, a necessary and sufficient condition is provided for the stabilization of a lossless negative imaginary system by a strictly negative imaginary controller. Finally, a flexible structure example is presented to illustrate the theory. [Copyright &y& Elsevier]

Abstract: This paper proposes a robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties. An eigenstate of the two-level quantum system is identified as a sliding mode. The objective is to design a control law to steer the system’s state into the sliding mode domain and then maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. We propose a controller design method using the Lyapunov methodology and periodic projective measurements. In particular, we give conditions for designing such a control law, which can guarantee the desired robustness in the presence of the uncertainties. The sliding mode control method has potential applications to quantum information processing with uncertainties. [Copyright &y& Elsevier]

Abstract: In this paper, an LQG control problem is solved for a class of linear quantum systems for the case of sampled-data measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. [Copyright &y& Elsevier]

Abstract: This paper presents a method for approximating a class of complex transfer function matrices corresponding to physically realizable complex linear quantum systems. The class of linear quantum systems under consideration includes interconnections of passive optical components such as cavities, beam-splitters, phase-shifters and interferometers. This approximation method builds on a previous result for cascade realization and gives good approximations at low frequencies. [Copyright &y& Elsevier]