Robust Stability of Quantum Systems with Nonlinear Dynamic Uncertainties

This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of coupling operators and a quadratic Hamiltonian. This paper extends previous results on the robust stability of nonlinear quantum systems to allow for quantum systems with dynamic uncertainties. These dynamic uncertainties are required to satisfy a certain quantum stochastic integral quadratic constraint. The robust stability condition is given in terms of a strict bounded real condition. This result is applied to the robust stability analysis of an optical parametric amplifier.Comment: A shortened version is to appear in the proceedings of the 2013 IEEE Conference on Decision and Contro

A Popov Stability Condition for Uncertain Linear Quantum Systems

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.Comment: A shortened version to appear in the proceedings of the 2013 American Control Conferenc

Robust Mean Square Stability of Open Quantum Stochastic Systems with Hamiltonian Perturbations in a Weyl Quantization Form

This paper is concerned with open quantum systems whose dynamic variables satisfy canonical commutation relations and are governed by quantum stochastic differential equations. The latter are driven by quantum Wiener processes which represent external boson fields. The system-field coupling operators are linear functions of the system variables. The Hamiltonian consists of a nominal quadratic function of the system variables and an uncertain perturbation which is represented in a Weyl quantization form. Assuming that the nominal linear quantum system is stable, we develop sufficient conditions on the perturbation of the Hamiltonian which guarantee robust mean square stability of the perturbed system. Examples are given to illustrate these results for a class of Hamiltonian perturbations in the form of trigonometric polynomials of the system variables.Comment: 11 pages, Proceedings of the Australian Control Conference, Canberra, 17-18 November, 2014, pp. 83-8

Performance Analysis and Coherent Guaranteed Cost Control for Uncertain Quantum Systems Using Small Gain and Popov Methods

This technical note extends applications of the quantum small gain and Popov methods from existing results on robust stability to performance analysis results for a class of uncertain quantum systems. This class of systems involves a nominal linear quantum system and is subject to quadratic perturbations in the system Hamiltonian. Based on these two methods, coherent guaranteed cost controllers are designed for a given quantum system to achieve improved control performance. An illustrative example also shows that the quantum Popov approach can obtain less conservative results than the quantum small gain approach for the same uncertain quantum system.This work was supported by the Australian Research Council (DP130101658, FL110100020

Quantum Popov robust stability analysis of an optical cavity containing a saturated Kerr medium

This paper applies results on the robust stability of nonlinear quantum systems to a system consisting an optical cavity containing a saturated Kerr medium. The system is characterized by a Hamiltonian operator which contains a non-quadratic term involving a quartic function of the annihilation and creation operators. A saturated version of the Kerr nonlinearity leads to a sector bounded nonlinearity which enables a quantum small gain theorem to be applied to this system in order to analyze its stability. Also, a non-quadratic version of a quantum Popov stability criterion is presented and applied to analyze the stability of this system.Comment: A shortened version will appear in the Proceedings of the 2013 European Control Conferenc

Guaranteed Non-quadratic Performance for Quantum Systems with Nonlinear Uncertainties

This paper presents a robust performance analysis result for a class of uncertain quantum systems containing sector bounded nonlinearities arising from perturbations to the system Hamiltonian. An LMI condition is given for calculating a guaranteed upper bound on a non-quadratic cost function. This result is illustrated with an example involving a Josephson junction in an electromagnetic cavity.Comment: A version of this paper is to appear in the Proceedings of the 2014 American Control Conferenc

Quantum Robust Stability of a Small Josephson Junction in a Resonant Cavity

This paper applies recent results on the robust stability of nonlinear quantum systems to the case of a Josephson junction in a resonant cavity. The Josephson junction is characterized by a Hamiltonian operator which contains a non-quadratic term involving a cosine function. This leads to a sector bounded nonlinearity which enables the previously developed theory to be applied to this system in order to analyze its stability.Comment: A version of this paper appeared in the proceedings of the 2012 IEEE Multi-conference on Systems and Contro