Linear Multivariable Control

1. Front Matter

   Pages N2-X

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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

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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.

• Mathematica
• algebra
• linear algebra
• matrix
• optimization
• stabilization
• system

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

  Walter Murray Wonham

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