Mathematical systems theory: 1 Modelling, state space analysis, stability and robustness
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2005
|
| Series: | Texts in applied mathematics
48 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Auch als Internetausgabe |
| Physical Description: | XV, 804 S. graph. Darst. |
| ISBN: | 3540441255 |
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IMAGE 1
DIEDERICH HINRICHSEN ANTHONY J. PRITCHARD
MATHEMATICAL
SYSTEMS THEORY I MODELLING, STATE SPACE ANALYSIS, STABILITY AND
ROBUSTNESS
WITH 180 FIGURES
FYA SPRINGER
IMAGE 2
CONTENTS
PREFACE VII
1 MATHEMATICAL MODELS 1
1.1 POPULATION DYNAMICS 2
1.1.1 NOTES AND REFERENCES 6
1.2 ECONOMICS 8
1.2.1 NOTES AND REFERENCES 12
1.3 MECHANICS 13
1.3.1 TRANSLATIONAL MECHANICAL SYSTEMS 13
1.3.2 MECHANICAL SYSTEMS WITH ROTATIONAL ELEMENTS 18
1.3.3 THE VARIATIONAL METHOD 27
1.3.4 NOTES AND REFERENCES 38
1.4 ELECTROMAGNETISM AND ELECTRICAL SYSTEMS 39
1.4.1 MAXWELL'S EQUATIONS AND THE ELEMENTS OF ELECTRICAL CIRCUITS 39
1.4.2 ELECTRICAL NETWORKS 50
1.4.3 NOTES AND REFERENCES 55
1.5 DIGITAL SYSTEMS 56
1.5.1 COMBINATIONAL SWITCHING NETWORKS 59
1.5.2 SEQUENTIAL SWITCHING NETWORKS 62
1.5.3 NOTES AND REFERENCES 68
1.6 HEAT TRANSFER 70
1.6.1 NOTES AND REFERENCES 72
2 INTRODUCTION TO STATE SPACE THEORY 73
2.1 DYNAMICAL SYSTEMS 74
2.1.1 THE GENERAL CONCEPT OF A DYNAMICAL SYSTEM 74
2.1.2 DIFFERENTIABLE DYNAMICAL SYSTEMS 83
2.1.3 SYSTEM PROPERTIES 88
2.1.4 LINEARIZATION 92
2.1.5 EXERCISES 94
2.1.6 NOTES AND REFERENCES # 98
2.2 LINEAR SYSTEMS 100
2.2.1 GENERAL LINEAR SYSTEMS 100
2.2.2 FREE MOTIONS OF TIME-INVARIANT LINEAR DIFFERENTIAL SYSTEMS 104
2.2.3 FREE MOTIONS OF TIME-INVARIANT LINEAR DIFFERENCE SYSTEMS 113 2.2.4
INFINITE DIMENSIONAL SYSTEMS 115
2.2.5 EXERCISES 121
2.2.6 NOTES AND REFERENCES 123
2.3 LINEAR SYSTEMS: INPUT-OUTPUT BEHAVIOUR 124
IMAGE 3
XII CONTENTS
2.3.1 INPUT-OUTPUT BEHAVIOUR IN TIME DOMAIN 124
2.3.2 TRANSFER FUNCTIONS 138
2.3.3 RELATIONSHIP BETWEEN INPUT-OUTPUT OPERATORS AND TRANSFER MATRICES
147
2.3.4 EXERCISES 151
2.3.5 NOTES AND REFERENCES 153
2.4 TRANSFORMATIONS AND INTERCONNECTIONS 154
2.4.1 MORPHISMS AND STANDARD CONSTRUCTIONS 154
2.4.2 COMPOSITE SYSTEMS 160
2.4.3 EXERCISES 166
2.4.4 NOTES AND REFERENCES 167
2.5 SAMPLING AND APPROXIMATION 168
2.5.1 A/D- AND D/A-CONVERSION OF SIGNALS 169
2.5.2 THE SAMPLING THEOREM 171
2.5.3 SAMPLING CONTINUOUS TIME SYSTEMS 175
2.5.4 APPROXIMATION OF CONTINUOUS SYSTEMS BY DISCRETE SYSTEMS 177 2.5.5
EXERCISES 189
2.5.6 NOTES AND REFERENCES 192
3 STABILITY THEORY 193
3.1 GENERAL DEFINITIONS 194
3.1.1 LOCAL FLOWS 195
3.1.2 STABILITY DEFINITIONS 199
3.1.3 LIMIT SETS 202
3.1.4 RECURRENCE 206
3.1.5 ATTRACTORS 211
3.1.6 EXERCISES 213
3.1.7 NOTES AND REFERENCES . . . 215
3.2 LIAPUNOV'S DIRECT METHOD 217
3.2.1 GENERAL DEFINITIONS AND RESULTS 217
3.2.2 TIME-VARY ING FINITE DIMENSIONAL SYSTEMS 229
3.2.3 TIME-INVARIANT SYSTEMS 235
3.2.4 EXERCISES 248
3.2.5 NOTES AND REFERENCES 251
3.3 LINEARIZATION AND STABILITY 253
3.3.1 STABILITY CRITERIA FOR TIME-VARYING LINEAR SYSTEMS 254
3.3.2 TIME-INVARIANT SYSTEMS: SPECTRAL STABILITY CRITERIA 263
3.3.3 NUMERICAL STABILITY OF DISCRETIZATION METHODS 268
3.3.4 LIAPUNOV FUNCTIONS FOR TIME-VARYING LINEAR SYSTEMS 272
3.3.5 LIAPUNOV FUNCTIONS FOR TIME-INVARIANT LINEAR SYSTEMS 282 3.3.6
EXERCISES 291
3.3.7 NOTES AND REFERENCES 295
3.4 STABILITY CRITERIA FOR POLYNOMIALS 296
3.4.1 STABILITY CRITERIA AND THE ARGUMENT PRINCIPLE 297
3.4.2 CHARACTERIZATION OF STABILITY VIA THE CAUCHY INDEX 308
3.4.3 HERMITE FORMS AND BEZOUTIANTS 313
3.4.4 HANKEL MATRICES AND RATIONAL FUNCTIONS 320
3.4.5 APPLICATIONS TO STABILITY 334
3.4.6 SCHUR POLYNOMIALS ? 340
IMAGE 4
CONTENTS XIII
3.4.7 ALGEBRAIC STABILITY DOMAINS AND LINEAR MATRIX EQUATIONS 357 3.4.8
EXERCISES 361
3.4.9 NOTES AND REFERENCES 366
4 PERTURBATION THEORY 369
4.1 PERTURBATION OF POLYNOMIALS 369
4.1.1 DEPENDENCE OF THE ROOTS ON THE COEFFICIENT VECTOR 370
4.1.2 POLYNOMIALS WITH HOLOMORPHIC COEFFICIENTS 376
4.1.3 THE SETS OF HURWITZ AND SCHUR POLYNOMIALS 384
4.1.4 KHARITONOV'S THEOREM 389
4.1.5 EXERCISES , 393
4.1.6 NOTES AND REFERENCES 396
4.2 PERTURBATION OF MATRICES 398
4.2.1 CONTINUITY AND ANALYTICITY OF EIGENVALUES 398
4.2.2 ESTIMATES FOR EIGENVALUES AND GROWTH RATES 404
4.2.3 SMOOTHNESS OF EIGENPROJECTIONS AND EIGENVECTORS 409
4.2.4 EXERCISES 426
4.2.5 NOTES AND REFERENCES 429
4.3 THE SINGULAR VALUE DECOMPOSITION 431
4.3.1 SINGULAR VALUES AND SINGULAR VECTORS 431
4.3.2 SINGULAR VALUE DECOMPOSITION 435
4.3.3 MATRICES DEPENDING ON A REAL PARAMETER 439
4.3.4 RELATIONS BETWEEN EIGENVALUES AND SINGULAR VALUES 444
4.3.5 EXERCISES 446
4.3.6 NOTES AND REFERENCES 448
4.4 STRUCTURED PERTURBATIONS 449
4.4.1 ELEMENTS OF /I-ANALYSIS 449
4.4.2 /I-VALUES FOR REAL FULL-BLOCK PERTURBATIONS 465
4.4.3 EXERCISES 480
4.4.4 NOTES AND REFERENCES 481
4.5 COMPUTATIONAL ASPECTS 484
4.5.1 CONDITION NUMBERS 485
4.5.2 MATRIX TRANSFORMATIONS 492
4.5.3 ALGORITHMS 501
4.5.4 EXERCISES 513
4.5.5 NOTES AND REFERENCES 515
5 UNCERTAIN SYSTEMS 517
5.1 MODELS OF UNCERTAINTY AND TOOLS FOR THEIR ANALYSIS 520
5.1.1 GENERAL DEFINITIONS AND BASIC PROPERTIES 520
5.1.2 PERTURBATION STRUCTURES * 530
5.1.3 EXERCISES 540
5.1.4 NOTES AND REFERENCES 542
5.2 SPECTRAL VALUE SETS 544
5.2.1 GENERAL DEFINITIONS AND RESULTS 544
5.2.2 COMPLEX FULL-BLOCK PERTURBATIONS 556
5.2.3 REAL FULL-BLOCK PERTURBATIONS 561
5.2.4 THE UNSTRUCTURED CASE (PSEUDOSPECTRA) 569
5.2.5 EXERCISES % 580
IMAGE 5
R CONTENTS
5.2.6 NOTES AND REFERENCES 583
5.3 STABILITY RADII 585
5.3.1 GENERAL DEFINITIONS AND RESULTS 586
5.3.2 COMPLEX FULL-BLOCK PERTURBATIONS 591
5.3.3 REAL FULL-BLOCK PERTURBATIONS 596
5.3.4 HAMILTONIAN CHARACTERIZATION OF THE COMPLEX STABILITY RADIUS . . .
602 5.3.5 THE UNSTRUCTURED CASE 609
5.3.6 DEPENDENCE ON SYSTEM DATA 614
5.3.7 STABILITY RADII AND THE CAYLEY TRANSFORMATION 617
5.3.8 EXERCISES 621
5.3.9 NOTES AND REFERENCES 624
5.4 ROOT SETS AND STABILITY RADII OF POLYNOMIALS 625
5.4.1 GENERAL FORMULAS 625
5.4.2 COMPLEX PERTURBATION STRUCTURES 633
5.4.3 REAL PERTURBATION STRUCTURES 637
5.4.4 EXERCISES 644
5.4.5 NOTES AND REFERENCES 646
5.5 TRANSIENT BEHAVIOUR 648
5.5.1 TRANSIENT BOUNDS AND INITIAL GROWTH RATE 648
5.5.2 CONTRACTIONS AND ESTIMATES OF THE TRANSIENT BOUND 658
5.5.3 SPECTRAL VALUE SETS AND TRANSIENT BEHAVIOUR 669
5.5.4 ROBUSTNESS OF (M, ^-STABILITY 675
5.5.5 EXERCISES 680
5.5.6 NOTES AND REFERENCES 684
5.6 MORE GENERAL PERTURBATION CLASSES 686
5.6.1 THE PERTURBATION CLASSES 687
5.6.2 STABILITY RADII 696
5.6.3 THE AIZERMAN CONJECTURE 701
--.6.4 EXERCISES 709
5.6.5 NOTES AND REFERENCES 711
APPENDIX 715
A.I LINEAR ALGEBRA 715
A.I.I NORMS OF VECTORS AND MATRICES 715
A.1.2 SPECTRA AND DETERMINANTS 719
A. 1.3 REAL REPRESENTATION OF COMPLEX MATRICES 720
A. 1.4 DIRECT SUMS AND KRONECKER PRODUCTS 720
A.I.5 HERMITIAN MATRICES 722
A.2 COMPLEX ANALYSIS 724
A.2.1 TOPOLOGICAL PRELIMINARIES 724
A.2.2 PATH INTEGRALS 725
A.2.3 HOLOMORPHIC FUNCTIONS 727
A.2.4 ISOLATED SINGULARITIES A 729
A.2.5 ANALYTIC CONTINUATION 732
A.2.6 MAXIMUM PRINCIPLE AND SUBHARMONIC FUNCTIONS 733
A.3 CONVOLUTIONS AND TRANSFORMS 735
A.3.1 SEQUENCES: CONVOLUTION AND Z-TRANSFORMS 735
A.3.2 LEBESGUE SPACES, CONVOLUTION OF FUNCTIONS, LAPLACE TRANSFORMS . .
739 A.3.3 FOURIER SERIES AND FOURIER TRANSFORMS . 744
IMAGE 6
CONTENTS XV
A.3.4 HARDY SPACES 750
A.4 LINEAR OPERATORS AND LINEAR FORMS 753
A.4.1 SUMMABILITY AND GENERALIZED FOURIER SERIES 753
A.4.2 LINEAR OPERATORS ON BANACH SPACES 754
A.4.3 LINEAR OPERATORS ON HILBERT SPACES 757
A.4.4 SPECTRAL THEORY 759
REFERENCES 763
GLOSSARY 789
INDEX 795 |
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| indexdate | 2024-09-05T00:08:53Z |
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| language | English |
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| spelling | Hinrichsen, Diederich 1939- Verfasser (DE-588)122537289 aut Mathematical systems theory 1 Modelling, state space analysis, stability and robustness Diederich Hinrichsen ; Anthony J. Pritchard Berlin [u.a.] Springer 2005 XV, 804 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 48 Texts in applied mathematics ... Auch als Internetausgabe Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Systemtheorie (DE-588)4058812-9 gnd rswk-swf Systemtheorie (DE-588)4058812-9 s DE-604 Kontrolltheorie (DE-588)4032317-1 s Pritchard, Anthony J. 1937-2007 Verfasser (DE-588)140478280 aut (DE-604)BV019271619 1 Texts in applied mathematics 48 (DE-604)BV002476038 48 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012035072&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hinrichsen, Diederich 1939- Pritchard, Anthony J. 1937-2007 Mathematical systems theory Texts in applied mathematics Kontrolltheorie (DE-588)4032317-1 gnd Systemtheorie (DE-588)4058812-9 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4058812-9 |
| title | Mathematical systems theory |
| title_auth | Mathematical systems theory |
| title_exact_search | Mathematical systems theory |
| title_full | Mathematical systems theory 1 Modelling, state space analysis, stability and robustness Diederich Hinrichsen ; Anthony J. Pritchard |
| title_fullStr | Mathematical systems theory 1 Modelling, state space analysis, stability and robustness Diederich Hinrichsen ; Anthony J. Pritchard |
| title_full_unstemmed | Mathematical systems theory 1 Modelling, state space analysis, stability and robustness Diederich Hinrichsen ; Anthony J. Pritchard |
| title_short | Mathematical systems theory |
| title_sort | mathematical systems theory modelling state space analysis stability and robustness |
| topic | Kontrolltheorie (DE-588)4032317-1 gnd Systemtheorie (DE-588)4058812-9 gnd |
| topic_facet | Kontrolltheorie Systemtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012035072&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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