Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects

1. Front Matter

   Pages i-xv

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2. Introduction

   • Michel Gevers, Gang Li

   Pages 1-21

3. Finite Word Length errors and computations

   • Michel Gevers, Gang Li

   Pages 23-44

4. Parametrizations in digital system design

   • Michel Gevers, Gang Li

   Pages 45-83

5. Frequency weighted optimal design

   • Michel Gevers, Gang Li

   Pages 85-107

6. A new transfer function sensitivity measure

   • Michel Gevers, Gang Li

   Pages 109-125

7. Pole and zero sensitivity minimization

   • Michel Gevers, Gang Li

   Pages 127-158

8. A synthetic sensitivity — roundoff design

   • Michel Gevers, Gang Li

   Pages 159-181

9. Sparse optimal and suboptimal realizations

   • Michel Gevers, Gang Li

   Pages 183-215

10. Parametrizations in control problems

    • Michel Gevers, Gang Li

    Pages 217-259

11. Synthetic FWL compensator design

    • Michel Gevers, Gang Li

    Pages 261-287

12. Parametrizations in the Delta operator

    • Michel Gevers, Gang Li

    Pages 289-318

13. Generalized transfer function parametrizations for adaptive estimation

    • Michel Gevers, Gang Li

    Pages 319-358

14. Back Matter

    Pages 359-373

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This book is all about finite wordlength errors in digital filters, con­ trollers and estimators, and how to minimize the deleterious effects of these errors on the performance of these devices. This does by no means imply that all about finite wordlength errors in filters, controllers and estimators is to be found in this book. We first ventured into the world of finite wordlength effects in 1987 when Gang Li began his PhD thesis in this area. Our more experienced readers might well say 'This shows', but we believe that the extent of our new contributions largely offsets our relative inexperience about the subject that might surface here and there in the book. Our naive view on the subject of finite wordlength errors in 1987 could probably be summarized as follows: • numerical errors due to finite wordlength encoding and roundoff are something that one has to live with, and there is probably not much that can be done about them except to increase the wordlength by improvements on the hardware; • these errors are as old as finite arithmetic and numerical analysis and they must therefore be well understood by now; • thus, if something can be done to minimize their effects, it must have been analysed and put into practice a long time ago. It is almost fair to say that we were wrong on all counts.

• Normal
• algorithms
• calculus
• control
• design
• digital signal processing
• filtering
• filters
• information
• operator
• scaling
• signal
• signal processing
• simulation
• transformation

• Centre for Systems Engineering and Applied Mechanics (CESAME), Université Catholique de Louvain, Bâtiment Euler, Louvain-la-Neuve, Belgium

  Michel Gevers

• School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore

  Gang Li

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