Skip to main content
SpringerLink
Log in

Linear Multivariable Control

A Geometric Approach

  • Book
  • © 1974

Overview

Authors:
  1. Walter Murray Wonham

    1. Department of Electrical Engineering, University of Toronto, Toronto, Canada

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (14 chapters)

  1. Front Matter

    Pages N2-X
    Download chapter PDF

  2. Mathematical Preliminaries

    • Walter Murray Wonham
    Pages 1-34

  3. Introduction to Controllability

    • Walter Murray Wonham
    Pages 35-45

  4. Controllability, Feedback and Pole Assignment

    • Walter Murray Wonham
    Pages 46-54

  5. Observability and Dynamic Observers

    • Walter Murray Wonham
    Pages 55-89

  6. Disturbance Decoupling and Output Stabilization

    • Walter Murray Wonham
    Pages 90-104

  7. Controllability Subspaces

    • Walter Murray Wonham
    Pages 105-132

  8. Tracking and Regulation I: Output Stabilization

    • Walter Murray Wonham
    Pages 133-151

  9. Tracking and Regulation II: Internal Stabilization

    • Walter Murray Wonham
    Pages 152-183

  10. Tracking and Regulation III: Structurally Stable Synthesis

    • Walter Murray Wonham
    Pages 184-226

  11. Noninteracting Control: Basic Principles

    • Walter Murray Wonham
    Pages 227-247

  12. Noninteracting Control II: Efficient Compensation

    • Walter Murray Wonham
    Pages 248-276

  13. Noninteracting Control III: Generic Solvability

    • Walter Murray Wonham
    Pages 277-290

  14. Quadratic Optimization I: Existence and Uniqueness

    • Walter Murray Wonham
    Pages 291-305

  15. Quadratic Optimization II: Dynamic Response

    • Walter Murray Wonham
    Pages 306-327

  16. Back Matter

    Pages 328-347
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Department of Electrical Engineering, University of Toronto, Toronto, Canada

    Walter Murray Wonham

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation