Control Theory and Design: An RH2 and RH Viewpoint
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Table of contents
- Contentsv
- Preface & Acknowledgmentsix
- Chapter 1. Introduction1
- Chapter 2. Preliminaries3
- 2.1 Introduction3
- 2.2 Notation and terminology4
- 2.3 Polynomial matrices5
- 2.4 Proper rational matrices15
- 2.5 Poles and zeros26
- 2.6 Singular values40
- 2.7 Basic facts on linear operators43
- 2.8 Functional spaces of rational matrices45
- 2.9 Notes and references68
- Chapter 3. Feedback Systems Stability69
- 3.1 Introduction69
- 3.2 Internal and external stability70
- 3.3 Double coprime factorizations74
- 3.4 The set of stabilizing controllers80
- 3.5 Notes and references86
- Chapter 4. RH2 Control87
- 4.1 Introduction87
- 4.2 The full information problem89
- 4.3 The output estimation problem105
- 4.4 The partial information problem112
- 4.5 Notes and references119
- Chapter 5. RH₶ Control121
- 5.1 Introduction121
- 5.2 The standard problem125
- 5.3 The full information problem137
- 5.4 The output estimation problem156
- 5.5 The partial information problem166
- 5.6 The operatorial approach182
- 5.7 Notes and references193
- Chapter 6. Nonclassical Problems in RH2 and RH₶195
- 6.1 Introduction195
- 6.2 Parameter Space Optimization195
- 6.3 Mixed RH2 / RHα control223
- 6.4 RH2 control with regional pole placement235
- 6.5 Time-domain specifications242
- 6.6 Controllers with structural constraints250
- 6.7 Notes and references261
- Chapter 7. Uncertain Systems Control Design263
- 7.1 Introduction263
- 7.2 Robust stability and performance263
- 7.3 Actuators failure285
- 7.4 Nonlinear perturbations289
- 7.5 Notes and references300
- A. Some Facts on Polynomials301
- B. Singular Values of Matrices303
- C. Riccati Equation315
- D. Structural Properties325
- E. The Standard 2-Block Scheme327
- F. Loop Shifting337
- G. Worst Case Analysis343
- H. Convex Functions and Sets349
- I. Convex Programming Numerical Tools359
- Bibliography371
- Index375
Control systems design methodologies have long suffered the traditional and myopic dichotomy between time and frequency domain approaches, each of them being specialized to cope with only scarcely overlapping performance requirements. This book is aimed at bridging the two approaches by presenting design methodologies based on the minimization of a norm (H2/H() of a suitable transfer function. A distinctive feature of these techniques is the fact that they do not create only one solution to the design problem, instead they provide a whole set of admissible solutions which satisfy a constraint on the maximum deterioration of the performance index.
A systematic book on this topic is long overdue. Self-contained and practical in its approach, Control Theory and Design enables the reader to use the relevant techniques in various real-life applications. The text covers the basic facts of robustcontrol and theory as well as more recent achievements, such as robust stability and robust performance in presence of parameter uncertainties. It features a new perspective on classical LQC results and further sections on robust synthesis, nonclassicaloptimization problems, and analysis and synthesis of uncertain systems.
Control Theory and Design is essential reading for graduates and those entering the research field. The required mathematical background is provided so that the book is also suitable for undergraduate students with some knowledge of basic systemsand control.
Key Features
* Provides a self-contained manual for learning control systems and design
* Contains a clear and concise presentation of the technical background needed
* Includes a new perspective of classical LQG results
* Contains updated results and novel contributions to nonstandard RH2/RH infinity symbol problems
* Covers all the theory from the basic to the more advanced issues
A systematic book on this topic is long overdue. Self-contained and practical in its approach, Control Theory and Design enables the reader to use the relevant techniques in various real-life applications. The text covers the basic facts of robustcontrol and theory as well as more recent achievements, such as robust stability and robust performance in presence of parameter uncertainties. It features a new perspective on classical LQC results and further sections on robust synthesis, nonclassicaloptimization problems, and analysis and synthesis of uncertain systems.
Control Theory and Design is essential reading for graduates and those entering the research field. The required mathematical background is provided so that the book is also suitable for undergraduate students with some knowledge of basic systemsand control.
Key Features
* Provides a self-contained manual for learning control systems and design
* Contains a clear and concise presentation of the technical background needed
* Includes a new perspective of classical LQG results
* Contains updated results and novel contributions to nonstandard RH2/RH infinity symbol problems
* Covers all the theory from the basic to the more advanced issues