© 1979

Linear Multivariable Control: a Geometric Approach


Part of the Applications of Mathematics book series (SMAP, volume 10)

Table of contents

  1. Front Matter
    Pages i-xv
  2. W. Murray Wonham
    Pages 1-35
  3. W. Murray Wonham
    Pages 36-47
  4. W. Murray Wonham
    Pages 48-56
  5. W. Murray Wonham
    Pages 57-85
  6. W. Murray Wonham
    Pages 86-101
  7. W. Murray Wonham
    Pages 102-128
  8. W. Murray Wonham
    Pages 129-145
  9. W. Murray Wonham
    Pages 215-233
  10. W. Murray Wonham
    Pages 234-256
  11. W. Murray Wonham
    Pages 257-269
  12. W. Murray Wonham
    Pages 284-304
  13. Back Matter
    Pages 305-327

About this book


In writing this monograph my aim has been to present a "geometric" approach to the structural synthesis of multivariable control systems that are linear, time-invariant and of finite dynamic order. The book is addressed to graduate students specializing in control, to engineering scientists engaged in control systems research and development, and to mathemati­ cians with some previous acquaintance with control problems. The present edition of this book is a revision of the preliminary version, published in 1974 as a Springer-Verlag "Lecture Notes" volume; and some of the remarks to follow are repeated from the original preface. The label "geometric" in the title is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometric) style. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometric properties of distinguished state subspaces. Indeed, the geometry was first brought in out of revulsion against the orgy of matrix manipulation which linear control theory mainly consisted of, not so long ago. But secondly and of greater interest, the geometric setting rather quickly suggested new methods of attacking synthesis which have proved to be intuitive and econo­ mical; they are also easily reduced to matrix arithmetic as soon as you want to compute.


Control Kontrolle Mathematica algebra algorithms linear algebra matrices matrix optimization polynomial programming stability stabilization system

Authors and affiliations

  1. 1.Department of Electrical EngineeringUniversity of TorontoTorontoCanada

Bibliographic information

  • Book Title Linear Multivariable Control: a Geometric Approach
  • Authors W. M. Wonham
  • Series Title Applications of Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York 1979
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-90354-5
  • Softcover ISBN 978-1-4684-0070-0
  • eBook ISBN 978-1-4684-0068-7
  • Series ISSN 0172-4568
  • Edition Number 2
  • Number of Pages , 0
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published as Volume 101 in the series: Lecture Notes in Economics and Mathematical Systems
  • Topics Systems Theory, Control
    Calculus of Variations and Optimal Control; Optimization
  • Buy this book on publisher's site
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