The QFT robust performance problem in its entirety may be reduced to an H problem by casting each specification as a frequency domain constraint either on the nominal sensitivity function or the complementary sensitivity function. In order to alleviate the conservative nature of a standard H solution that is obtainable for a plant with parametric uncertainty we develop a new stability criterion to replace the small gain condition. With this new stability criterion it is shown that the existence of a solution to the standard H problem guarantees a solution to the QFT problem. Specifically, we provide an explicit characterization of necessary frequency weighting functions for an H embedding of the QFT specifications. Due to the transparency in selecting the weighting functions, the robust performance constraints can be easily relaxed, if needed, for the purpose of assuring a solution to the H problem. Since this formulation provides only a sufficient condition for the existence of a QFT controller one can then use the resulting H compensator to initiate the QFT loop shaping step.

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