# Linear Multivariable Control

## A Geometric Approach

Book

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

1. Front Matter
Pages i-xvi
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 86-102
7. W. Murray Wonham
Pages 103-130
8. W. Murray Wonham
Pages 131-150
9. W. Murray Wonham
Pages 151-183
10. W. Murray Wonham
Pages 184-220
11. W. Murray Wonham
Pages 221-239
12. W. Murray Wonham
Pages 240-262
13. W. Murray Wonham
Pages 263-275
14. W. Murray Wonham
Pages 276-289
15. W. Murray Wonham
Pages 290-310
16. Back Matter
Pages 311-334

### Introduction

In wntmg 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 ad­ dressed to graduate students specializing in control, to engineering scientists involved in control systems research and development, and to mathemati­ cians interested in systems control theory. 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 prop­ erties 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, around fifteen years ago. But secondly and of greater interest, the geometric setting rather quickly sug­ gested new methods of attacking synthesis which have proved to be intuitive and economical; they are also easily reduced to matrix arithmetic as soon as you want to compute. The essence of the "geometric" 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 Y. Then, if all is well, you may calculate F from Y quite easily.

### Keywords

Control Kontrolle (Math.) algorithms optimization programming 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 Applications of Mathematics
• DOI https://doi.org/10.1007/978-1-4612-1082-5
• Copyright Information Springer-Verlag New York Inc. 1985
• Publisher Name Springer, New York, NY
• eBook Packages
• Hardcover ISBN 978-0-387-96071-5
• Softcover ISBN 978-1-4612-7005-8
• eBook ISBN 978-1-4612-1082-5
• Series ISSN 0172-4568
• Edition Number 3
• Number of Pages XVI, 334
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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