An H{sub}∞ formulation of quantitative feedback theory

摘要

The QFT robust performance problem in its entirety may be reduced to an H{sub}∞ problem by casting each specification as a frequency domain constraint either on the nominal sensitivity function or the complementary sensitivity function. In orderto alleviate the conservative nature of a standard H{sub}∞ 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 thatthe existence of a solution to the standard H{sub}∞ problem guarantees a solution to the QFT problem. Specifically, we provide an explicit characterization of necessary frequency weighting functions for an H{sub}∞ embedding of the QFT specifications.Due to The transparency in selecting the weighting functions, the robust performance constraints can be easily relaxe4, if needed, for the purpose of assuring a solution to the H{sub}∞problem. Since this formulation provides only a sufficient conditionfor the existence of a QFT controller one can then use the resulting H{sub}∞ compensator to initiate the QFT loop shaping step.