  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 case of a nominal linear quantum system is considered with
non-quadratic perturbations to the system Hamiltonian. The paper extends recent
results on the robust stability of nonlinear quantum systems to allow for
non-quadratic perturbations to the Hamiltonian which depend on multiple
parameters. A robust stability condition is given in terms of a strict bounded
real condition. This result is then applied to the robust stability analysis of
a nonlinear quantum system which is a model of an optical parametric amplifier.
