Stability of linear systems : some aspects of kinematic similarity / C.J. Harris and J.F. Miles.

Format:

Book

Author/Creator:

Harris, C. J. (Christopher John)

Contributor:

Miles, J. F.

Series:

Mathematics in science and engineering ; v. 153.

Mathematics in science and engineering ; v. 153

Language:

English

Subjects (All):

System analysis.

Stability.

Physical Description:

1 online resource (247 p.)

Place of Publication:

London ; New York : Academic Press, 1980.

Language Note:

English

Summary:

Stability of linear systems : some aspects of kinematic similarity

Contents:

Front Cover; Stability of Linear Systems: Some Aspects of Kinematic Similarity; Copyright Page; Preface; Contents; Chapter 1. Mathematical Preliminaries; 1.1 Metric Spaces; 1.2 Normed Metric Spaces; 1.3 Contraction Mappings; 1.4 Linear Operators; 1.5 Linear Transformations and Matrices; 1.6 Inner Product Spaces and Fourier Series; 1.7 Notes; References; Chapter 2. Almost Periodic Functions; 2.1 Introduction; 2.2 Definitions and Elementary Properties of Almost Periodic Functions; 2.3 Mean Values of Almost Periodic Functions and their Fourier Series

2.4 Almost Periodic Functions Depending Uniformly on a Parameter2.5 Bochner's Criterion; 2.6 Limiting Cases of Almost Periodic Functions; 2.7 Notes; References; Chapter 3. Properties of Ordinary Differential Equations; 3.1 Introduction; 3.2 Existence and Uniqueness of Solution; 3.3 Linear Ordinary Differential Equations; 3.4 Constant Coefficient Differential Equations; 3.5 Periodic Coefficients and Floquet Theory; 3.6 Notes; 3.7 References; Chapter 4. Kinematic Similarity; 4.1 Introduction; 4.2 Liapunov Transformations and Kinematic Similarity; 4.3 Invariants and Canonical Forms

4.4 Necessary and Sufficient Conditions for Kinematic Similarity4.5 Estimates for Characteristic Exponents; References; Chapter 5. Stability Theory for Nonstationary Systems; 5.1 Local Equilibrium Stability Conditions; 5.2 Asymptotic Stability; 5.3 Matrix Projections and Dichotomies of Linear Systems; 5.4 Asymptotic Characteristic Value Stability Theory; 5.5 Stability in the Large; 5.6 Total Stability and Stability under Disturbances; 5.7 Sufficient Conditions for Stability; 5.8 Notes and Input-Output Stability; References; Chapter 6. Asymptotic Floquet Theory; 6.1 Introduction

6.2 The Cappel-Bohr Lemma and Linear Differential Equations with Almost Periodic Coefficients6.3 Coppel's Theorem; 6.4 Almost Periodic Matrices Containing a Parameter; References; Chapter 7. Linear Systems with Variable Coefficients; 7.1 Introduction and Survey of Applications; 7.2 Beam Stabilisation in an Alternating Gradient Proton Synchrotron; References; Appendix 1. Existence of Solutions to Periodic and Almost Periodic Differential Systems; Appendix 2. Dichotomies and Kinematic Similarity; Appendix 3. Bibliography; Subject Index

Notes:

Description based upon print version of record.

Includes bibliography and index.

ISBN:

1-282-29026-6

9786612290268

0-08-095661-0

OCLC:

316552957