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Frequency Domain Properties of Scalar and Multivariable Feedback Systems

  • Book
  • © 1988

Overview

Editors:
  1. James Scott Freudenberg
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  2. Douglas Paul Looze
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Part of the book series: Lecture Notes in Control and Information Sciences (LNCIS, volume 104)

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Table of contents (13 chapters)

  1. Front Matter

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  2. Introduction

    Pages 1-11

  3. Review of classical results

    Pages 12-28

  4. Tradeoffs in the design of scalar linear time-invariant feedback systems

    Pages 29-55

  5. Comments on design methodologies

    Pages 56-73

  6. Multivariable systems: Summary of existing results and motivation for further work

    Pages 74-99

  7. Gain, phase, and directions in multivariable systems

    Pages 100-113

  8. The relation between open loop and closed loop properties of multivariable feedback systems

    Pages 114-140

  9. Singular values and analytic function theory

    Pages 141-152

  10. Structure of the complex unit sphere and singular vectors

    Pages 153-178

  11. Differential equations for singular vectors and failure of the Cauchy-Riemann equations

    Pages 179-201

  12. A multivariable gain-phase relation

    Pages 202-218

  13. An example illustrating the multivariable gain-phase relation

    Pages 219-249

  14. Conclusions

    Pages 250-251

  15. Back Matter

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Keywords

About this book

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.

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