Finite Frequency Analysis and Synthesis for Singularly Perturbed Systems

1. Front Matter

   Pages i-xiv

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2. Preliminaries

   1. Front Matter

      Pages 1-1

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   2. Singular Perturbation Methods and Time-Scale Techniques

      • Chenxiao Cai, Zidong Wang, Jing Xu, Yun Zou

      Pages 3-27

   3. Theoretical Foundation of Finite Frequency Control

      • Chenxiao Cai, Zidong Wang, Jing Xu, Yun Zou

      Pages 29-47

3. Singularly Perturbed Systems Analysis and Synthesis

   1. Front Matter

      Pages 49-49

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   2. Stabilization of Singularly Perturbed Systems

      • Chenxiao Cai, Zidong Wang, Jing Xu, Yun Zou

      Pages 51-65

   3. Finite Frequency \(H_\infty \) Control for Singularly Perturbed Systems

      • Chenxiao Cai, Zidong Wang, Jing Xu, Yun Zou

      Pages 67-118

   4. Finite Frequency Positive Real Control for Singularly Perturbed Systems

      • Chenxiao Cai, Zidong Wang, Jing Xu, Yun Zou

      Pages 119-136

   5. The Sensitivity-Shaping Problem for Singularly Perturbed Systems

      • Chenxiao Cai, Zidong Wang, Jing Xu, Yun Zou

      Pages 137-177

4. Applications

   1. Front Matter

      Pages 179-179

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   2. Applications

      • Chenxiao Cai, Zidong Wang, Jing Xu, Yun Zou

      Pages 181-224

5. Back Matter

   Pages 225-227

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This book is a self-contained collection of recent research findings providing a comprehensive and systematic unified framework for both analysis and synthesis for singularly perturbed systems. It paves the way for the gap between frequency-domain-transfer-function-based results and time-domain-state-space-based results to be bridged.

It is divided into three parts focusing on: fundamental background of singular perturbation; general singular perturbation methodologies and time-scale techniques and the theoretical foundation of finite-frequency control; the analysis and synthesis of singularly perturbed systems; and real-world engineering applications implementing the results developed in systems like wind turbines and autonomous-aerial-vehicle hovering.

It also presents solutions to analysis and design problems in terms of linear matrix inequalities. Lastly, it provides valuable reference material for researchers who wish to explore the design of controllers for such systems.

• Singularly Perturbed Systems
• Finite Frequency Control
• H-infinity Control
• Positive Real Control
• Mixed H_/H-infinity Control

“This book focuses on recent research findings providing a comprehensive and systematic, unified framework for both analysis and synthesis of singularly perturbed systems. … the authors provide analysis and synthesis of singularly perturbed systems. They present real-world engineering applications implementing the results developed, like wind turbines and autonomous-aerial-vehicle hovering. Most solutions are given in terms of linear matrix inequalities.” (V. A. Sobolev, Mathematical Reviews, March, 2019)​

• School of Automation, Nanjing University of Science and Technology, Nanjing, China

  Chenxiao Cai, Jing Xu, Yun Zou

• Department of Computer Science, Brunel University, Uxbridge, United Kingdom

  Zidong Wang

Chenxiao Cai was born in Shandong, China, in 1975. She received the Ph.D. degree in control theory and control engineering from the School of Automation, Nanjing University of Science and Technology, Nanjing, China in 2005. She is currently a Professor with the School of Automation, Nanjing University of Science and Technology, Nanjing, China. Her current research interests include singularly perturbed systems, singular systems, complex networks, finite frequency and unmanned aerial vehicles.

Zidong Wang was born in Jiangsu, China, in 1966. He received the B.Sc. degree in mathematics in 1986 from Suzhou University, Suzhou, China, and the M.Sc. degree in applied mathematics in 1990 and the Ph.D. degree in electrical engineering in 1994, both from Nanjing University of Science and Technology, Nanjing, China.

He is currently Professor of Dynamical Systems and Computing in the Department of Information Systems and Computing, Brunel University, U.K. From 1990 to 2002, he held teaching and research appointments in universities in China, Germany and the UK. Prof. Wang's research interests include dynamical systems, signal processing, bioinformatics, control theory and applications. He has published more than 300 papers in refereed international journals. He is a holder of the Alexander von Humboldt Research Fellowship of Germany, the JSPS Research Fellowship of Japan, William Mong Visiting Research Fellowship of Hong Kong.

Professor Wang is an IEEE Fellow. He serves as an Associate Editor for 12 international journals, including IEEE Transactions on Automatic Control, IEEE Transactions on Control Systems Technology, IEEE Transactions on Neural Networks, IEEE Transactions on Signal Processing, and IEEE Transactions on Systems, Man, and Cybernetics - Part C. He is a Fellow of the IEEE, a Fellow of the Royal Statistical Society and a member of program committee for many international conferences.

Jing Xu was born in Jiangsu, China, in 1990. Shereceived the B.S. degree in Science from Nanjing University of Science and Technology, Nanjing, China, in 2012. She is currently pursuing the Ph.D. degree in control theory and control engineering from the School of Automation, Nanjing University of Science and Technology, Nanjing, China. Her current research interests include singularly perturbed systems, fault detection, finite frequency control, and unmanned aerial vehicles.

Yun Zou was born in Jiangsu, China, in 1962. He received the B.S. degree in mathematics from Northwestern University, Xi’an, China, in 1983, and the M.S. and Ph.D. degree in control theory and control engineering from Nanjing University of Science and Technology, Nanjing, China, in 1987 and in 1990, respectively. Now he is a Professor in the School of Automation at the Nanjing University of Science and Technology, Nanjing, China. His research interests include differential-algebraic equation system, two dimensional systems and neural networks.

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