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

摘要

This paper is concerned with open quantum systems whose dynamic variablessatisfy canonical commutation relations and are governed by quantum stochasticdifferential equations. The latter are driven by quantum Wiener processes whichrepresent external boson fields. The system-field coupling operators are linearfunctions of the system variables. The Hamiltonian consists of a nominalquadratic function of the system variables and an uncertain perturbation whichis represented in a Weyl quantization form. Assuming that the nominal linearquantum system is stable, we develop sufficient conditions on the perturbationof the Hamiltonian which guarantee robust mean square stability of theperturbed system. Examples are given to illustrate these results for a class ofHamiltonian perturbations in the form of trigonometric polynomials of thesystem variables.