# Classical Control Using H-Infinity MethodsTheory, Optimization, and Design

## $43.99 (C) • Date Published: January 1987 • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability. • format: Paperback • isbn: 9780898714197 ##$43.99 (C) Paperback

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• This versatile book teaches control system design using H-Infinity techniques that are simple and compatible with classical control, yet powerful enough to quickly allow the solution of physically meaningful problems. The authors begin by teaching how to formulate control system design problems as mathematical optimization problems and then discuss the theory and numerics for these optimization problems. Their approach is simple and direct, and since the book is modular, the parts on theory can be read independently of the design parts and vice versa, allowing readers to enjoy the book on many levels. Until now, there has not been a publication suitable for teaching the topic at the undergraduate level. This book fills that gap by teaching control system design using H-Infinity techniques at a level within reach of the typical engineering and mathematics student. It also contains a readable account of recent developments and mathematical connections.

## Reviews & endorsements

'The books by Helton and Merino contain a wealth of material that can be used by students and researchers in a variety of different ways, depending on background and interests. To enhance this modular flexibility, the authors offer two versions … Both versions contain introductory material, at an elementary level, on what control engineering is all about …' Joseph A. Ball, SIAM Review

'This book, treating control system design using H-Infinity techniques and H-Infinity theory motivated by control applications, is a very good tool for a large number of people interested in control and in H^\infty theory, from undergraduate students and engineers to research mathematicians. Here the reader can find answers to practical and theoretical problems, even by a partial reading, because the book is written in a highly modular way …' I. Valusescu, Zentralblatt für Mathematik

' The authors make clear that a powerful and unified theory of H-Infinity design is beginning to emerge, but that much remains to be done. The present book is a welcome contribution that should help to publicize the important advances that have been made and their potential for solving a difficult class of engineering control design problems.' N. Harris McClamroch, Mathematical Reviews

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## Product details

• Date Published: January 1987
• format: Paperback
• isbn: 9780898714197
• length: 308 pages
• dimensions: 250 x 177 x 16 mm
• weight: 0.537kg
• availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.

Preface
Part I. Short Design Course:
1. A Method for Solving System Design Problems
2. Internal Stability
3. Frequency Domain Performance Requirements
4. Optimization
Review of Concepts
5. A Design Example With OPTDesign
Part II. More on Design:
6. Examples
7. Internal Stability
Part III. H-Infinity Theory:
8. H^\infty Optimization and Control
11. Proof of the Main Result
12. Computer Solutions to OPT
Part IV. H-Infinity Theory. Vector Case. 13. Many Analytic Functions
14. Coordinate Descent Approaches to OPT
15. More Numerical Algorithms
16. More Theory of the Vector OPT Problem
Part V. Semidefinite Programming vs. H-Infinity Optimization. 17. Matrix H-Infinity Optimization
18. Numerical Algorithms for H-Infinity Optimization
19. Semidefinite Programming vs. Matrix H-Infinity Optimization
20. Proofs
Part VI. Appendices: Appendix A. History and Perspective
Appendix B. Pure Mathematics and H-Infinity Optimization
Appendix C. Uncertainty
Appendix D. Computer Code for Examples in 6
Appendix E. Getting OPTDesign and Anopt
Appendix F. Anopt Notebook
Appendix G. NewtonInterpolant Notebook
Appendix H. NewtonFit Notebook..

• ## Authors

J. William Helton, University of California, San Diego

Orlando Merino, University of Rhode Island

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