Robust control theory in Hilbert space:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Springer
1998
|
| Schriftenreihe: | Applied mathematical sciences
130 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007892931&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 225 S. |
| ISBN: | 0387982914 |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface vii
1 Basic Hilbert Space Theory 1
1.1 Geometry of Hilbert Space 1
1.2 Basic Operator Theory 9
1.3 Banach Algebras 12
1.4 Exercises 18
2 Operator Theoretic Preliminaries 19
2.1 Functional Calculus for Self Adjoint Operators 19
2.2 Polar Decompositions 22
2.3 Weak Convergence in H 24
2.4 Operator Topologies 27
2.5 The Minimum Modulus of an Operator 29
2.6 Exercises: 30
3 A Distance Formula and Some Consequences 33
3.1 Operator Matrices 33
3.2 Multiplication Operators and Nehari s Theorem 38
3.3 NestAlgebras 47
3.4 Exercises 52
3.5 References, Notes, and Remarks 54
4 Factorization Theorems 55
4.1 Inner Outer Factorization in H2 55
xiv Contents
4.2 Inner Outer Factorizations in Nest Algebras 58
4.3 Cholesky Factorization 63
4.4 7 Spectral Factorizations 67
4.5 The Entropy Operator 72
4.6 Exercises 73
4.7 References, Notes, and Remarks 74
5 Linear Systems 77
5.1 The Extended Space of a Hilbert Space 77
5.2 Causality 80
5.3 Unbounded Linear Operators on H 82
5.4 Stable Systems 84
5.5 Exercises 85
5.6 References, Notes, and Remarks 86
6 Stabilization 87
6.1 Feedback Systems 87
6.2 Graph Representations 91
6.3 Representations and Strong Representations 93
6.4 Stabilization and Strong Representations 98
6.5 Construction of Coprime Factorizations from State Space Models 105
6.6 Strong and Simultaneous Stabilization 108
6.7 Exercises 113
6.8 References, Notes, and Remarks 114
7 Uniform Optimal Control 117
7.1 Sensitivity Minimization 117
7.2 The Scalar Commutant Lifting Theorem 119
7.3 Uniform Optimal Control for Time Varying Systems 122
7.4 Solving the Model Matching Problem 128
7.5 Maximizing the Entropy Operator 132
7.6 Application to Time Varying Sampled Data Systems 135
7.7 Exercises 140
7.8 References, Notes, and Remarks 141
8 Robustness of Time Varying Systems 143
8.1 Proper Representation Uncertainty 143
8.2 Maximal Stabilizable Operator Balls 148
8.3 Uniform Robust Stability 155
8.4 Exercises 163
8.5 References, Notes, and Remarks 163
9 The Gap Metric and Internal Stability 165
9.1 Directed Gaps and Gaps 165
9.2 Gap Balls 168
9.3 Properties of the Gap Metric 172
Contents xv
9.4 The Gap Metric and Robustness 175
9.5 Stability and the Gap Metric 176
9.6 Exercises 182
9.7 References, Notes, and Remarks 184
10 Robust Stabilization in the Gap Metric 187
10.1 The Gap and the 2 block Problem 187
10.2 Maximally Stabilizing Controllers 190
10.3 More on a(Lx,L2) 194
10.4 The Gap Metric and Coprime Factor Perturbations 197
10.5 Exercises 204
10.6 References, Notes, and Remarks 204
11 Orthogonal Embedding of Time Varying Systems 207
11.1 The Time Invariant Case 207
11.2 Causality on H © H 209
11.3 Isometric 4 block Extensions 210
11.4 Strict Contractions 211
11.5 Special Cases and Examples 213
11.6 Exercises 215
11.7 References, Notes, and Remarks 216
Index 217
|
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:17:13Z |
| institution | BVB |
| isbn | 0387982914 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007892931 |
| oclc_num | 845440365 |
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| owner_facet | DE-20 DE-355 DE-BY-UBR DE-29T DE-83 DE-11 |
| physical | XV, 225 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spellingShingle | Feintuch, Avraham Robust control theory in Hilbert space Applied mathematical sciences Kontrolltheorie (DE-588)4032317-1 gnd Zeitvariantes System (DE-588)4190654-8 gnd Operatortheorie (DE-588)4075665-8 gnd Hilbert-Raum (DE-588)4159850-7 gnd Robuste Kontrolle (DE-588)4232797-0 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4190654-8 (DE-588)4075665-8 (DE-588)4159850-7 (DE-588)4232797-0 |
| title | Robust control theory in Hilbert space |
| title_auth | Robust control theory in Hilbert space |
| title_exact_search | Robust control theory in Hilbert space |
| title_full | Robust control theory in Hilbert space Avraham Feintuch |
| title_fullStr | Robust control theory in Hilbert space Avraham Feintuch |
| title_full_unstemmed | Robust control theory in Hilbert space Avraham Feintuch |
| title_short | Robust control theory in Hilbert space |
| title_sort | robust control theory in hilbert space |
| topic | Kontrolltheorie (DE-588)4032317-1 gnd Zeitvariantes System (DE-588)4190654-8 gnd Operatortheorie (DE-588)4075665-8 gnd Hilbert-Raum (DE-588)4159850-7 gnd Robuste Kontrolle (DE-588)4232797-0 gnd |
| topic_facet | Kontrolltheorie Zeitvariantes System Operatortheorie Hilbert-Raum Robuste Kontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007892931&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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