InhaltsangabeReview of classical results.- Tradeoffs in the design of scalar linear time-invariant feedback systems.- Comments on design methodologies.- Multivariable systems: Summary of existing results and motivation for further work.- Gain, phase, and directions in multivariable systems.- The relation between open loop and closed loop properties of multivariable feedback systems.- Singular values and analytic function theory.- Structure of the complex unit sphere and singular vectors.- Differential equations for singular vectors and failure of the Cauchy-Riemann equations.- A multivariable gain-phase relation.- An example illustrating the multivariable gain-phase relation.- Conclusions.