Stability of linear systems : some aspects of kinematic similarity /
Harris, C. J.
Stability of linear systems : some aspects of kinematic similarity / C.J. Harris and J.F. Miles. - London ; New York : Academic Press, 1980. - 1 online resource (vii, 236 pages) : illustrations - Mathematics in science and engineering ; v. 153 . - Mathematics in science and engineering ; v. 153. .
Includes bibliographical references (pages 220-231) and index.
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
Stability of linear systems : some aspects of kinematic similarity.
9780123282507 (electronic bk.) 0123282500 (electronic bk.) 9780080956619 (electronic bk.) 0080956610 (electronic bk.)
System analysis.
Stability.
Linear systems.
Systems Analysis
Analyse de systèmes.
Stabilité.
Systèmes linéaires.
systems analysis.
stability.
SCIENCE--System Theory.
TECHNOLOGY & ENGINEERING--Operations Research.
Linear systems.
Stability.
System analysis.
Electronic books.
Electronic books.
QA402 / .H34 1980eb
003
Stability of linear systems : some aspects of kinematic similarity / C.J. Harris and J.F. Miles. - London ; New York : Academic Press, 1980. - 1 online resource (vii, 236 pages) : illustrations - Mathematics in science and engineering ; v. 153 . - Mathematics in science and engineering ; v. 153. .
Includes bibliographical references (pages 220-231) and index.
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
Stability of linear systems : some aspects of kinematic similarity.
9780123282507 (electronic bk.) 0123282500 (electronic bk.) 9780080956619 (electronic bk.) 0080956610 (electronic bk.)
System analysis.
Stability.
Linear systems.
Systems Analysis
Analyse de systèmes.
Stabilité.
Systèmes linéaires.
systems analysis.
stability.
SCIENCE--System Theory.
TECHNOLOGY & ENGINEERING--Operations Research.
Linear systems.
Stability.
System analysis.
Electronic books.
Electronic books.
QA402 / .H34 1980eb
003