Qualitative Analysis of Large Scale Dynamical Systems

Name: Qualitative Analysis of Large Scale Dynamical Systems
Brand: Academic Press
Price: 71.95 EUR
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Michel(Autor*in)

Michel(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

307 Seiten

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978-0-08-095643-5 (ISBN)

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Inhalt

Front Cover
Qualitative Analysis of Large Scale Dynamical Systems
Copyright Page
Contents
Preface
Acknowledgments
Chapter I. Introduction
1.1 Introduction
1.2 Qualitative Analysis of Dynarnical Systems: General Remarks
1.3 Qualitative Analysis of Large Scale Systems: General Remarks
1.4 An Overview of the Subsequent Chapters
Chapter II. Systems Described by Ordinary Differential Equations
2.1 Notation
2.2 Lyapunov Stability and Related Results
2.3 Large Scale Systems
2.4 Analysis by Scalar Lyapunov Functions
2.5 Application of M-Matrices
2.6 Application of the Comparison Principle to Vector Lyapunov Functions
2.7 Estimates of Trajectory Behavior and Trajectory Bounds
2.8 Applications
2.9 Notes and References
Chapter III. Discrete Time Systems and Sampled Data Systems
3.1 Systems Described by Difference Equations
3.2 Large Scale Systems
3.3 Stability and Instability of Large Scale Systems
3.4 Examples
3.5 Sampled Data Systems
3.6 Notes and References
Chapter IV. Systems Described by Stochastic Differential Equations
4.1 Notation
4.2 Systems Described by Stochastic Differential Equations
4.3 Composite Systems
4.4 Analysis by Scalar Lyapunov Functions
4.5 Analysis by Vector Lyapunov Functions
4.6 Examples
4.7 Notes and References
Chapter V. Infinite-Dimensional Systems
5.1 Notation
5.2 Co-Semigroups
5.3 Nonlinear Semigroups
5.4 Lyapunov Stability of Dynamical Systems
5.5 Examples of Semigroups
5.6 Stability of Large Scale Systems Described on Banach Spaces
5.7 Some Examples and Applications
5.8 Functional Differential Equations-Special Results
5.9 Application of Comparison Theorems to Vector Lyapunov Functions
5.10 Notes and References
Chapter VI. Input-Output Stability of Large Scale Systems
6.1 Preliminaries
6.2 Stability of Large Scale Systems: Results Involving Gains
6.3 Instability of Large Scale Systems
6.4 Stability of Large Scale Systems: Results Involving Sector and Conicity Conditions
6.5 Stability of Large Scale Systems: Popov-Like Conditions
6.6 L8-Stability and l8-Stability of Large Scale Systems
6.7 Analysis and Design Procedure
6.8 Notes and References
Chapter VII. Integrodifferential Systems
7.1 Preliminary Results
7.2 L2-Stability and Instability of Interconnected Systems
7.3 Linear Equations and Linearized Equations
7.4 An Example
7.5 Notes and References
References
Index

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