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This paper concerns a class of uncertain linear quantum systems subject toquadratic perturbations in the system Hamiltonian. A small gain approach isused to evaluate the performance of the given quantum system. In order to getimproved control performance, we propose two methods to design a coherentcontroller for the system. One is to formulate a static quantum controller byadding a controller Hamiltonian to the given system, and the other is to builda dynamic quantum controller which is directly coupled to the given system.Both controller design methods are given in terms of LMIs and a non-convexequality. Hence, a rank constrained LMI method is used as a numericalprocedure. An illustrative example is given to demonstrate the proposed methodsand also to make a performance comparison with different controller designmethods. Results show that for the same uncertain quantum system, the dynamicquantum controller can offer an improvement in performance over the staticquantum controller.

Guaranteed Cost Dynamic Coherent Control for Uncertain Linear Quantum Systems