内容简介：　　　

　　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; 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.

英文目录：
1 Introduction
　　1.1 Two-Dimensional Systems
　　　　1.1.1 Preliminary Background
　　　　1.1.2 Analysis and Synthesis of 2-D Discrete Systems
　　　　1.1.3 Some Classes of 2-D Systems
　　1.2 Linear Repetitive Processes
　　　　1.2.1 Preliminary Background
　　　　1.2.2 Stability Analysis and Control of LRPs
　　1.3 Outline of the Book
Part I General Theory of Some Classes of 2-D Systems
2 Robust Filtering of 2-D Uncertain State-Delayed Systems
　　2.1 Introduction
　　2.2 System Description and Preliminaries
　　2.3 Main Results
　　　　2.3.1 Filtering Analysis
　　　　2.3.2 Filter Design
　　2.4 Further Extensions
　　　　2.4.1 Polytopic Uncertain Case
　　　　2.4.2 Norm-Bounded Uncertain Case
　　2.5 Illustrative Example
　　2.6 Conclusion
3 Robust Filtering of 2-D Linear Parameter-Varying Systems
　　3.1 Introduction
　　3.2 System Description and Preliminaries
　　3.3 H∞ Filtering
　　3.4 1-∞Filtering
　　3.5 Illustrative Example
　　3.6 Conclusion
4 Filter Design Approach to Fault Detection of 2-D Markovian Jump Systems
　　4.1 Introduction
　　4.2 System Description and Preliminaries
　　4.3 Main Results
　　　　4.3.1 Performance Analysis
　　　　4.3.2 Fault Detection Filter Design
　　4.4 Illustrative Example
　　4.5 Conclusion
5 Dynamic Output Feedback Control of 2-D Linear Parameter-Varying Systems
　　5.1 Introduction
　　5.2 Problem Formulation and Preliminaries
　　5.3 Main Results
　　5.4 Illustrative Example
　　5.5 Conclusion
6 Sliding Mode Control of 2-D Systems
　　6.1 Introduction
　　6.2 System Description and Preliminaries
　　6.3 2-D Reaching Law
　　6.4 SMC Design: Method I
　　6.5 SMC Design: Method II
　　6.6 Illustrative Example
　　6.7 Conclusion
7 Model Approximation of 2-D State-Delayed Systems
　　7.1 Introduction
　　7.2 Problem Formulation and Preliminaries
　　7.3 Main Results
　　　　7.3.1 Single Delay Case
　　　　7.3.2 Multiple Delay Case
　　7.4 Illustrative Example
　　7.5 Conclusion
Part II A Special Class of 2-D Systems: Linear Repetitive Processes
8 Robust Filtering of Differential and Discrete LRPs
　　8.1 Introduction
　　8.2 Filtering of Differential LRPs
　　　　8.2.1 Problem Formulation
　　　　8.2.2 Main Results
　　　　8.2.3 Extension to Uncertain Case
　　　　8.2.4 Illustrative Example
　　8.3 Filtering of Discrete LRPs
　　　　8.3.1 Problem Formulation
　　　　8.3.2 Main Results
　　　　8.3.3 Illustrative Example
　　8.4 Conclusion
9 Reduced-Order H2 Filter Design for Discrete LRPs
　　9.1 Introduction
　　9.2 Problem Formulation and Preliminaries
　　9.3 H2 Performance Analysis
　　9.4 Full-Order H2 Filter Design
　　9.5 Reduced-Order H2 Filter Design
　　　　9.5.1 Convex Linearization Approach
　　　　9.5.2 Projection Approach
　　9.6 Illustrative Example
　　9.7 Conclusion
10 Filter Design Approach to Fault Detection of Discrete LRPs
　　10.1 Introduction
　　10.2 Problem Formulation and Preliminaries
　　10.3 Main Results
　　10.4 Illustrative Example
　　10.5 Conclusion
11 Dynamic Output Feedback Control of Differential and Discrete LRPs
　　11.1 Introduction
　　11.2 Differential LRPs Case
　　　　11.2.1 Problem Formulation and Preliminaries
　　　　11.2.2 Generalized H2 Performance Analysis
　　　　11.2.3 Generalized H2 Static Feedback Control
　　　　11.2.4 Generalized H2 Dynamic Output Feedback Control
　　　　11.2.5 Illustrative Example
　　11.3 Discrete LRPs Case
　　　　11.3.1 Problem Formulation and Preliminaries
　　　　11.3.2 Performances Analysis
　　　　11.3.3 H1 Dynamic Output Feedback Control
　　　　11.3.4 Generalized H2 Dynamic Output Feedback Control
　　　　11.3.5 Illustrative Example
　　11.4 Conclusion
12 State Estimation and Quasi Sliding Mode Control of Differential LRPs
　　12.1 Introduction
　　12.2 Problem Formulation and Preliminaries
　　12.3 Main Results
　　　　12.3.1 Analysis of Sliding Mode Process
　　　　12.3.2 Observer and SMC Law Design
　　　　12.3.3 Reachability Analysis
　　12.4 Illustrative Example
　　12.5 Conclusion
13 Model Approximation of Differential and Discrete LRPs
　　13.1 Introduction
　　13.2 Differential LRPs Case
　　　　13.2.1 Problem Formulation
　　　　13.2.2 Hankel-Norm Performance
　　　　13.2.3 Hankel-Norm Model Approximation
　　　　13.2.4 A Special Case
　　　　13.2.5 Illustrative Example
　　13.3 Discrete LRPs Case
　　　　13.3.1 Problem Formulation
　　　　13.3.2 Hankel-Norm Performance
　　　　13.3.3 Hankel-Norm Model Approximation
　　　　13.3.4 A Special Case
　　　　13.3.5 Illustrative Example
　　13.4 Conclusion
14 Conclusion and Further Work
　　14.1 Conclusion
　　14.2 Further Work
References