Mathematical systems theory: 1 Modelling, state space analysis, stability and robustness
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Edition: | 1st. ed. 2005, 1st. corr. softcover print. 2010 |
| Series: | Texts in applied mathematics
48 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 763 - 788 |
| Physical Description: | XV, 804 S. graph. Darst. |
| ISBN: | 9783642039409 |
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MARC
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| 245 | 1 | 0 | |a Mathematical systems theory |n 1 |p Modelling, state space analysis, stability and robustness |c Diederich Hinrichsen ; Anthony J. Pritchard |
| 250 | |a 1st. ed. 2005, 1st. corr. softcover print. 2010 | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XV, 804 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Texts in applied mathematics |v 48 | |
| 490 | 0 | |a Texts in applied mathematics |v ... | |
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Record in the Search Index
| _version_ | 1809312575991578624 |
|---|---|
| adam_text |
Contents
Preface
vii
Mathematical Models
і
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
. 2?
1.
3.4
Notes and References
.,. 38
1.4
Electromagnetism
and Electrical Systems
. 39
1.4.1
Maxwell's liquations 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
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
Exerciser
.,,,.,. 94
2.1.6
Notes and References
. 98
2.2
Linear
Systeme. 100
2.2.1
General Linear Systems
.,.,.,. 100
2.2.2
Free Motions of Time Invariant Linear Differential
Systeme.104
2.2.3
Free Motions of Time-invariant Linear Difference Systems
. 113
2.2.4
Infinite Dimensional Systems
. . . , ,.
lio
2.2.5
Exercises
.,.
L21
2.2.6
Notes and References
. 123
2.3
Linear Systems: Input-Output Behaviour
. 124
xi
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
Moi'phisras 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
Attractora
.211
3.1.6
Exercises
.213
3.1.7
Notes and References
.215
3.2
Liapmiov's Direct Method
.217
3.2.1
General Definitions and Results
.217
3.2.2
Time-Varying 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
. 29
L
3.3.7
Notes and References
.295
3.4
Stability Criteria for Polynomials
. 296
3.4.1
Stability Criteria and the Argument Principle
, ,.
9.9'f
3.4.2
Characterization of Stability via the Cauciry Index
.308
3.4.3
Hermite Forms and
BézoiUiaiits
.313
3.4.4
Hankel
Matrices and Rational Functions
.320
3.4.5
Applications to Stability
.334
3.4.6 Schur
Polynomials
.340
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 Holomoiphic Coefficients
.376
4.1.3
The Sets of Hurwitz and
Schur
Polynomials
.384
4.1.4
Kliaritonov'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 Heal 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
μ-
Analysis
.449
4.4.2
μ-
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
ЅЈ.У
5.1
Models of Uncertainty and Tools for their Analysis
.520
o.J.l General Definitions and Basic Properties
.,,., 520
5.1.2
Perturbation Structures
. 530
5.1.3
Exercises
.,,.,., . 540
0.1.4
Notes and References
. 542
5.2
Spectral Value
Scî.s
.,.,,. 544
5.2.1
General Definition;.; 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 (Paeudospeetra)
. 569
5.2.5
Exercises
. 580
xiv 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
Hamilfconiaii 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
Cayîey
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.Ő
Noies
and References
.646
5.5
Transient Behaviour
.648
5.5.1
Transient Bounds and Initial Growth Rate
. 648
5,0.2
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
5.6.4
Exercises
.709
5.6.5
Notes and References
.711
Appendix
715
A.I Linear Algebra
.715
A.
1.1
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.
1.5
Hermitian Matrices
.722
A.
2
Complex Analysis
.724
A.
2.1
Topologica!
Preliminaries
.724
A.2.2 Path Integrals
.725
A.
2.3
Holomorphic Functions
.727
A.
2.4
Isolated Singularities
.729
A.
2.5
Analytic Continuation
.732
A.
2.6
.Maximum Principle and Subharmomc Functions
.733
A.3 Convolutions and Transforms
.735
A.
3.1
Sequences: Convolution and
й-
Transforms
.735
A.
3.2
Lebesgue Spaces, Convolution of Functions, Laplace Vransfoniis
. . 739
A.
3.3
Fourier Series and Fourier Transforms
.744
Contents xv
Α.
3.4
Hardy Spaces
.750
A.
4
Linear Operators and Linear Forms
.753
A.
4.1
Summabiiity and Generalized Fourier Series
.753
A.
4.2
Linear Operators on Banach Spaces
.754
A.
4.3
Linear Operators on Hubert Spaces
.757
A.4.4 Spectral Theory
.759
References
763
Glossary
789
Index
795 |
| any_adam_object | 1 |
| author | Hinrichsen, Diederich 1939- Pritchard, Anthony J. 1937-2007 |
| author_GND | (DE-588)122537289 (DE-588)140478280 |
| author_facet | Hinrichsen, Diederich 1939- Pritchard, Anthony J. 1937-2007 |
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| classification_rvk | SK 880 SK 960 |
| classification_tum | MSR 550f MAT 344f MAT 496f |
| ctrlnum | (OCoLC)574955827 (DE-599)BVBBV041903459 |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik |
| edition | 1st. ed. 2005, 1st. corr. softcover print. 2010 |
| format | Book |
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| id | DE-604.BV041903459 |
| illustrated | Illustrated |
| indexdate | 2024-09-05T00:08:54Z |
| institution | BVB |
| isbn | 9783642039409 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027347152 |
| oclc_num | 574955827 |
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| owner_facet | DE-11 DE-706 DE-898 DE-BY-UBR DE-91 DE-BY-TUM DE-739 |
| physical | XV, 804 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| 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 1st. ed. 2005, 1st. corr. softcover print. 2010 Berlin [u.a.] Springer 2010 XV, 804 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 48 Texts in applied mathematics ... Literaturverz. S. 763 - 788 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 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027347152&sequence=000002&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=027347152&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019271619 (DE-604)BV002476038 |
| work_keys_str_mv | AT hinrichsendiederich mathematicalsystemstheory1 AT pritchardanthonyj mathematicalsystemstheory1 |