Qualitative analysis of large scale dynamical systems / Anthony N. Michel, Richard K. Miller.

Format:

Book

Author/Creator:

Michel, Anthony N.

Contributor:

Miller, Richard K.

Series:

Mathematics in science and engineering ; 134.

Mathematics in science and engineering ; 134

Language:

English

Subjects (All):

System analysis.

System theory.

Physical Description:

1 online resource (307 p.)

Place of Publication:

New York : Academic Press, 1977.

Language Note:

English

Summary:

Qualitative analysis of large scale dynamical systems

Contents:

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 Functions2.7 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 Functions4.5 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 Systems6.1 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 Equations7.4 An Example; 7.5 Notes and References; References; Index

Notes:

Description based upon print version of record.

Includes bibliography and index.

ISBN:

1-282-29004-5

9786612290046

0-08-095643-2

OCLC:

466443974