Rubio / Booker / Declaris The Theory of Linear Systems

1. Auflage 2013
ISBN: 978-1-4832-1987-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 344 Seiten, Web PDF

The Theory of Linear Systems presents the state-phase analysis of linear systems. This book deals with the transform theory of linear systems, which had most of its success when applied to time-invariant systems. Organized into nine chapters, this book begins with an overview of the development of some properties of simple differential systems that are mostly of a nonalgebraic nature. This text then presents a brief treatment of vector spaces, matrices, transformations, norms, and inner products. Other chapters deal with the inductive process used to define dynamical systems. This book discusses as well the existence and uniqueness theorem for the solutions of a homogeneous linear differential system. The final chapter deals with the abstract concept of a dynamical system and derives properties of these systems. This book is a valuable resource for advanced graduate students in areas such as economics and bioengineering. Engineers engaged in systems design will also find this book useful.

Autoren/Hrsg.

Rubio, J. E.

Booker, Henry G.

Declaris, Nicholas

Inhaltsverzeichnis

1;Front Cover;1
2;The Theory of Linear Systems;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;Acknowledgments;12
7;Chapter 1. The Search for an Internal Structure;14
7.1;1.1. Introduction;14
7.2;1.2. The State of a System: An Example;18
7.3;1.3. Transfer Functions and State;20
7.4;1.4. Some Conclusions and a Program;29
8;Chapter 2. An Introduction to the Theory of Linear Spaces;36
8.1;2.1. Introduction;36
8.2;2.2. Sets and Operations on Sets;36
8.3;2.3. Functions;41
8.4;2.4. Linear Spaces;45
8.5;2.5. Basis and Dimension1;48
8.6;2.6. Linear Transformations and Matrices;53
8.7;2.7. Inverse Operators and Inverse Matrices;62
8.8;2.8. Metric Properties of Linear Spaces. Norms;70
8.9;2.9. Inner Products. Adjoint Operators;76
8.10;2.10. An Introduction t o Matrix Algebra;79
9;Chapter 3. Differential Systems I;84
9.1;3.1. Introduction;84
9.2;3.2. The Homogeneous System;87
9.3;3.3. Fundamental Matrices;94
9.4;3.4. The Transition Matrix;99
9.5;3.5. The Adjoint System;105
9.6;3.6. The General Solution of Nonhomogeneous Systems;107
9.7;3.7. A Summary and Some Conclusions;111
9.8;SUPPLEMENTARY NOTES AND REFERENCES;114
9.9;REFERENCES;114
10;Chapter 4. Differential Systems II;115
10.1;4.1. Introduction;115
10.2;4.2. Similarity, Eigenvalues, and Eigenvectors;116
10.3;4.3. Reduction;122
10.4;4.4. Diagonal ization;133
10.5;4.5. More on Reduction;138
10.6;4.6. Functions of Matrices;148
10.7;SUPPLEMENTARY NOTES AND REFERENCES;150
10.8;REFERENCES;150
11;Chapter 5. Controllability, Observability;151
11.1;5.1. Introduction;151
11.2;5.2. Controllability;152
11.3;5.3. A Necessary and Sufficient Condition for Controllability;156
11.4;5.4. A Necessary and Sufficient Condition for the Controllability of Constant Systems;161
11.5;5.5. Transformation and Controllability;165
11.6;5.6. Controllability and Transfer Functions;168
11.7;5.7. A Condition for the Controllability of Time-Varying Systems;170
11.8;5.8. Observability;172
11.9;5.9. The Controllability and Observability of Composite Systems;177
11.10;5.10. Normal Systems;179
11.11;5.11. Output Controllability;180
11.12;5.12. Total Controllability. Total Observability;180
11.13;5.13. The Attainable Set;183
11.14;5.14. The Phase-Canonical Form;184
11.15;SUPPLEMENTARY NOTES AND REFERENCES;185
11.16;REFERENCES;188
12;Chapter 6. Synthesis;189
12.1;6.1. Introduction;189
12.2;6.2. Some Results on the Synthesis of Weighting Patterns;193
12.3;6.3. Introduction to Synthesis;200
12.4;6.4. A Method of Synthesis;207
12.5;6.5. Analytic Systems;219
12.6;6.6. The Reduction to Minimal Order in the General Case;222
12.7;6.7. The Observer;226
12.8;SUPPLEMENTARY NOTES AND REFERENCES;230
12.9;REFERENCES;232
13;Chapter 7. Difference Systems;233
13.1;7.1. Introduction;233
13.2;7.2. The Homogeneous System;237
13.3;7.3. The Nonhomogeneous System;243
13.4;7.4. A Summary;246
13.5;7.5. Controllability, Observability;247
13.6;SUPPLEMENTARY NOTES AND REFERENCES;250
13.7;REFERENCE;251
14;Chapter 8. Stability;252
14.1;8.1. Introduction;252
14.2;8.2. The Stability of Constant Systems;255
14.3;8.3. Exponential Stability;262
14.4;8.4. External Stability, Controllability, Observability and Exponential Stability;267
14.5;8.5. The Stability of Difference Systems;275
14.6;SUPPLEMENTARY NOTES AND REFERENCES;276
14.7;REFERENCES;277
15;Chapter 9. Infinite Dimensions;278
15.1;9.1. Introduction;278
15.2;9.2. Some Further Mathematical Topics;279
15.3;9.3. Dynamical Systems;284
15.4;9.4. Semigroups and Infinitesimal Generators;293
15.5;9.5. Infinitesimal Generators and Resolvents;300
15.6;9.6. Homogeneous and Nonhomogeneous Systems;305
15.7;9.7. Systems with Boundary Controls;309
15.8;9.8. Hilbert Spaces;312
15.9;9.9. Controllability;317
15.10;9.10. Conclusion;320
15.11;SUPPLEMENTARY NOTES AND REFERENCES;321
15.12;REFERENCES;322
16;APPENDIX;323
16.1;A.I. Elementary Row and Column Operations;323
16.2;A.2. The Computation of Eigenvalues, Eigenvectors,
and t h e Matrix (./. — .)—1;328
16.3;A.3. The Computation of the Transition Matrices of Constant Systems;332
16.4;A.4. Positive Definite Matrices;333
16.5;REFERENCES;334
17;Author Index;336
18;Subject Index;339