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This paper extends applications of the quantum small gain and Popov methodsfrom existing results on robust stability to performance analysis results for aclass of uncertain quantum systems. This class of systems involves a nominallinear quantum system and is subject to quadratic perturbations in the systemHamiltonian. Based on these two methods, coherent guaranteed cost controllersare designed for a given quantum system to achieve improved controlperformance. An illustrative example also shows that the quantum Popov approachcan obtain less conservative results than the quantum small gain approach forthe same uncertain quantum system.

Performance Analysis and Coherent Guaranteed Cost Control for Uncertain Quantum Systems Using Small Gain and Popov Methods