Algebraic versus analytic design limitations imposed by ill-conditioned plants

A long-standing conjecture has been that ill-conditioned multivariable plants pose an inherent design difficulty in that they limit the class of achievable robust performance specifications. The elusiveness of a proof of this conjecture has motivated study of an alternate design problem, involving only the nominal plant, in the hope that an inherent difficulty due to plant conditioning might emerge for this alternate problem. It is shown, under mild assumptions, that such a difficulty, if it indeed exists, must take the form of a design tradeoff between system properties at different frequencies, rather than between properties at the same frequency