Filtering and Control for Classes of Two-Dimensional Systems

1. Front Matter

   Pages i-xvi

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2. Introduction

   • Ligang Wu, Zidong Wang

   Pages 1-29

3. General Theory of Some Classes of 2-D Systems

   1. Front Matter

      Pages 31-31

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   2. Robust Filtering of 2-D Uncertain State-Delayed Systems

      • Ligang Wu, Zidong Wang

      Pages 33-55

   3. Robust Filtering of 2-D Linear Parameter-Varying Systems

      • Ligang Wu, Zidong Wang

      Pages 57-80

   4. Filter Design Approach to Fault Detection of 2-D Markovian Jump Systems

      • Ligang Wu, Zidong Wang

      Pages 81-105

   5. Dynamic Output Feedback Control of 2-D Linear Parameter-Varying Systems

      • Ligang Wu, Zidong Wang

      Pages 107-120

   6. Sliding Mode Control of 2-D Systems

      • Ligang Wu, Zidong Wang

      Pages 121-138

   7. Model Approximation of 2-D State-Delayed Systems

      • Ligang Wu, Zidong Wang

      Pages 139-167

4. A Special Class of 2-D Systems: Linear Repetitive Processes

   1. Front Matter

      Pages 169-169

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   2. Robust Filtering of Differential and Discrete LRPs

      • Ligang Wu, Zidong Wang

      Pages 171-195

   3. Reduced-Order \(\mathcal {H}_{2}\) Filter Design for Discrete LRPs

      • Ligang Wu, Zidong Wang

      Pages 197-216

   4. Filter Design Approach to Fault Detection of Discrete LRPs

      • Ligang Wu, Zidong Wang

      Pages 217-233

   5. Dynamic Output Feedback Control of Differential and Discrete LRPs

      • Ligang Wu, Zidong Wang

      Pages 235-265

   6. State Estimation and Quasi Sliding Mode Control of Differential LRPs

      • Ligang Wu, Zidong Wang

      Pages 267-281

   7. Model Approximation of Differential and Discrete LRPs

      • Ligang Wu, Zidong Wang

      Pages 283-322

   8. Conclusion and Further Work

      • Ligang Wu, Zidong Wang

      Pages 323-326

5. Back Matter

   Pages 327-336

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This book focuses on filtering, control and model-reduction problems for two-dimensional (2-D) systems with imperfect information. The time-delayed 2-D systems covered have system parameters subject to uncertain, stochastic and parameter-varying changes.

After an initial introduction of 2-D systems and the ideas of linear repetitive processes, the text is divided into two parts detailing:

· General theory and methods of analysis and optimal synthesis for 2-D systems; and

· Application of the general theory to the particular case of differential/discrete linear repetitive processes.

The methods developed provide a framework for stability and performance analysis, optimal and robust controller and filter design and model approximation for the systems considered. Solutions to the design problems are couched in terms of linear matrix inequalities.

For readers interested in the state of the art in linear filtering, control and model reduction, Filtering and Control for Classes of Two-Dimensional Systems will be a useful reference for exploring the field of 2-D systems either from a purely theoretical research perspective or from the point of view of a multitude of potential applications including image processing, and the study of seismographic data or thermal processes.

• 2-d Systems
• Linear Repetitive Processes
• Optimal Control
• Optimal Filtering
• Optimal Model Reduction
• Two-dimensional Systems

“This book presents up-to-date research developments and novel methodologies on linear two-dimensional (2-D) systems. … The book is addressed to postgraduate students and scientists.” (T. Kaczorek, Mathematical Reviews, July, 2015)

• Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, China

  Ligang Wu

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

  Zidong Wang

Zidong Wang is currently Professor of Dynamical Systems and Computing at Brunel University, West London, United Kingdom. From January 1997 to December 1998, he was an Alexander von Humboldt research fellow with the Control Engineering Laboratory, Ruhr-University Bochum, Germany. From January 1999 to February 2001, he was a Lecturer with the Department of Mathematics, University of Kaiserslautern, Germany. From March 2001 to July 2002, he was a University Senior Research Fellow with the School of Mathematical and Information Sciences, Coventry University, U.K. In August 2002, he joined the Department of Information Systems and Computing, Brunel University, U.K., as a Lecturer, and was then promoted to a Reader in September 2003 and to a Chair Professor in July 2007. Professor Wang's research interests include dynamical systems, signal processing, bioinformatics, control theory and applications. He has published more than 200 papers in refereed international journals. His publications have received more than 5000 citations (excluding self-citations) with h-index 48. He was awarded the Humboldt research fellowship in 1996 from Alexander von Humboldt Foundation, the JSPS Research Fellowship in 1998 from Japan Society for the Promotion of Science, and the William Mong Visiting Research Fellowship in 2002 from the University of Hong Kong.

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