# Linear Multivariable Control

## A Geometric Approach

Book

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 101)

1. Front Matter
Pages N2-X
2. Walter Murray Wonham
Pages 1-34
3. Walter Murray Wonham
Pages 35-45
4. Walter Murray Wonham
Pages 46-54
5. Walter Murray Wonham
Pages 55-89
6. Walter Murray Wonham
Pages 90-104
7. Walter Murray Wonham
Pages 105-132
8. Walter Murray Wonham
Pages 133-151
9. Walter Murray Wonham
Pages 152-183
10. Walter Murray Wonham
Pages 184-226
11. Walter Murray Wonham
Pages 227-247
12. Walter Murray Wonham
Pages 248-276
13. Walter Murray Wonham
Pages 277-290
14. Walter Murray Wonham
Pages 291-305
15. Walter Murray Wonham
Pages 306-327
16. Back Matter
Pages 328-347

### Introduction

In writing this monograph my objective is to present arecent, 'geometrie' 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 mathematicians with some previous acquaintance with control problems. The label 'geometrie' is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometrie) style. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometrie 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 secondlyand of greater interest, the geometrie setting rather quickly suggested new methods of attacking synthesis which have proved to be intuitive and economical; they are also easily reduced to matrix arith­ metic as soonas you want to compute. The essence of the 'geometrie' approach is just this: instead of looking directly for a feedback laW (say u = Fx) which would solve your synthesis problem if a solution exists, first characterize solvability as a verifiable property of some constructible state subspace, say J. Then, if all is weIl, you may calculate F from J quite easily.

### Keywords

Mathematica algebra linear algebra matrix optimization stabilization system

#### Authors and affiliations

1. 1.Department of Electrical EngineeringUniversity of TorontoTorontoCanada

### Bibliographic information

• Book Title Linear Multivariable Control
• Book Subtitle A Geometric Approach
• Authors W. M. Wonham
• Series Title Lecture Notes in Economics and Mathematical Systems
• DOI https://doi.org/10.1007/978-3-662-22673-5
• Copyright Information Springer-Verlag Berlin Heidelberg 1974
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Hardcover ISBN 978-3-540-06956-0
• Softcover ISBN 978-3-662-22675-9
• eBook ISBN 978-3-662-22673-5
• Series ISSN 0075-8442
• Edition Number 1
• Number of Pages X, 347
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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