ALGEBRAIC VERSUS ANALYTIC DESIGN LIMITATIONS IMPOSED BY ILL-CONDITIONED PLANTS

A long-standing conjecture has been that ill-conditioned multivariable plants pose inherent design difficulty in that they limit the class o f achievable robust performance specifications. The elusiveness of a p roof of this conjecture has motivated study of an alternate design pro blem, involving only the nominal plant, in the hope that an inherent d ifficulty due to plant conditioning might emerge for this alternate pr oblem. In this note we show, under mild assumptions, that such a diffi culty, if it indeed exists, must take the form of a design tradeoff be tween system properties at different frequencies, rather than between properties at the same frequency. (The terminology ''analytic'' and '' algebraic'' is motivated by the type of mathematics used to describe e ach class of tradeoff.) This analysis is also interpreted as implying the same conclusion for the original robust performance problem.