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This paper is concerned with a stochastic dissipativity theory usingquadratic-exponential storage functions for open quantum systems withcanonically commuting dynamic variables governed by quantum stochasticdifferential equations. The system is linearly coupled to external boson fieldsand has a quadratic Hamiltonian which is perturbed by nonquadratic functions oflinear combinations of system variables. Such perturbations are similar tothose in the classical Lur'e systems and make the quantum dynamics nonlinear.We study their effect on the quantum expectation of the exponential of apositive definite quadratic form of the system variables. This allowsconditions to be established for the risk-sensitive stochastic storage functionof the quantum system to remain bounded, thus securing boundedness for themoments of system variables of arbitrary order. These results employ anoncommutative analogue of the Doleans-Dade exponential and a multivariatepartial differential version of the Gronwall-Bellman lemma.

Risk-sensitive Dissipativity of Linear Quantum Stochastic Systems under Lur'e Type Perturbations of Hamiltonians