  This paper concerns a class of uncertain linear quantum systems subject to
quadratic perturbations in the system Hamiltonian. A small gain approach is
used to evaluate the performance of the given quantum system. In order to get
improved control performance, we propose two methods to design a coherent
controller for the system. One is to formulate a static quantum controller by
adding a controller Hamiltonian to the given system, and the other is to build
a dynamic quantum controller which is directly coupled to the given system.
Both controller design methods are given in terms of LMIs and a non-convex
equality. Hence, a rank constrained LMI method is used as a numerical
procedure. An illustrative example is given to demonstrate the proposed methods
and also to make a performance comparison with different controller design
methods. Results show that for the same uncertain quantum system, the dynamic
quantum controller can offer an improvement in performance over the static
quantum controller.
