Frequency Domain Properties of Scalar and Multivariable Feedback Systems

The purpose of this monograph is to present recent results concerning frequency response properties of linear feedback systems. The basic theme is to develop extensions of classical feedback theory from scalar to multivariable systems, and the obstacle is the fact that multivariable systems may possess properties having no scalar analogue. The monograph contains sections reviewing ideas from classical control theory that are extended to multivariable systems, a summary of work we have done on design limitation in scalar systems, and a review of some previous work on extending classical ideas to a multivariable setting. The bulk of the monograph develops analysis methods with which to study properties of multivariable systems having no scalar analogue. Although the monograph does contain expository material, its primary character is that of a research monograph, and its primary audience researchers in the field of linear multivariable control. Its contents should be accessible to a first year graduate student with a good knowledge of classical feedback theory.

Inhalt
Review 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.