Linear Multivariable Control

1. Front Matter

   Pages i-xvi

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2. Mathematical Preliminaries

   • W. Murray Wonham

   Pages 1-35

3. Introduction to Controllability

   • W. Murray Wonham

   Pages 36-47

4. Controllability, Feedback and Pole Assignment

   • W. Murray Wonham

   Pages 48-56

5. Observability and Dynamic Observers

   • W. Murray Wonham

   Pages 57-85

6. Disturbance Decoupling and Output Stabilization

   • W. Murray Wonham

   Pages 86-102

7. Controllability Subspaces

   • W. Murray Wonham

   Pages 103-130

8. Tracking and Regulation I: Output Regulation

   • W. Murray Wonham

   Pages 131-150

9. Tracking and Regulation II: Output Regulation with Internal Stability

   • W. Murray Wonham

   Pages 151-183

10. Tracking and Regulation III: Structurally Stable Synthesis

    • W. Murray Wonham

    Pages 184-220

11. Noninteracting Control I: Basic Principles

    • W. Murray Wonham

    Pages 221-239

12. Noninteracting Control II: Efficient Compensation

    • W. Murray Wonham

    Pages 240-262

13. Noninteracting Control III: Generic Solvability

    • W. Murray Wonham

    Pages 263-275

14. Quadratic Optimization I: Existence and Uniqueness

    • W. Murray Wonham

    Pages 276-289

15. Quadratic Optimization II: Dynamic Response

    • W. Murray Wonham

    Pages 290-310

16. Back Matter

    Pages 311-334

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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.

• Control
• Kontrolle (Math.)
• algorithms
• optimization
• programming
• system

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

  W. Murray Wonham

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