Interpolation of rational matrix functions:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel u.a.
Birkhäuser
1990
|
| Series: | Operator theory
45 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 605 S. |
| ISBN: | 3764324767 0817624767 |
Staff View
MARC
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| 100 | 1 | |a Ball, Joseph A. |d 1947- |e Verfasser |0 (DE-588)112083498 |4 aut | |
| 245 | 1 | 0 | |a Interpolation of rational matrix functions |c Joseph A. Ball ; Israel Gohberg ; Leiba Rodman |
| 264 | 1 | |a Basel u.a. |b Birkhäuser |c 1990 | |
| 300 | |a 605 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 45 | |
| 650 | 7 | |a Espaces d'interpolation |2 ram | |
| 650 | 7 | |a Interpolatie |2 gtt | |
| 650 | 7 | |a Matrices |2 gtt | |
| 650 | 7 | |a Matrices |2 ram | |
| 650 | 4 | |a fonction matricielle | |
| 650 | 4 | |a fonction rationnelle | |
| 650 | 4 | |a interpolation | |
| 650 | 4 | |a théorie interpolation | |
| 650 | 4 | |a théorie opérateur | |
| 650 | 4 | |a théorie système | |
| 650 | 4 | |a Interpolation spaces | |
| 650 | 4 | |a Matrices | |
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Record in the Search Index
| _version_ | 1804117085276602368 |
|---|---|
| adam_text | CONTENTS
PREFACE
INTRODUCTION 1
PART I HOMOGENEOUS INTERPOLATION PROBLEMS WITH
STANDARD DATA
1. Null Structure for Analytic Matrix Functions 7
1.1 Local null structure of analytic matrix function 7
1.2 Null chains and null pairs 14
1.3 Singular part and null subspace 24
1.4 Null triples 29
1.5 Null characteristics with respect to several zeros 35
2. Null Structure and Interpolation Problems for Matrix Polynomials 40
2.1 Local data 40
2.2 Linearization and monic matrix polynomials 42
2.3 Interpolation theorems: monic matrix polynomials with given null pairs 46
2.4 Interpolation of monic matrix polynomials with incomplete data 51
2.5 Non monic matrix polynomials with given null pairs 55
2.6 Pairs and triples 60
2.7 Proof of Theorem 1.4.3 64
3. Local Data for Meromorphic Matrix Functions 65
3.1 Null functions and pole functions 65
3.2 Null and pole chains, null and pole pairs 70
3.3 Null and pole triples and singular pairs 74
3.4 Local characteristics relative to several points 80
3.5 Local data at infinity and Mobius transformations 83
4. Rational Matrix Functions 86
4.1 Realizations and minimality 86
4.2 Realizations and local data 94
4.3 A global interpolation problem for rational matrix functions 97
4.4 Null pole coupling matrix 102
4.5 Interpolation with incomplete data: special case 106
4.6 Interpolation with incomplete data: general case 118
5. Rational Matrix Functions with Null and Pole Structure at Infinity 134
5.1 Realizations and Mobius transformations 134
5.2 Realizations of improper rational matrix functions 139
5.3 Null pole triples at infinity and Mobius transformations 142
5.4 Interpolation with data at infinity 145
5.5 Specializations for matrix polynomials 148
CONTENTS
5.6 Interpolation with prescribed null and pole data except at infinity 153
5.7 Minimal interpolation for matrix polynomials 160
6. Rational Matrix Functions with J Unitary Values on the Imaginary Line 162
6.1 Realization and interpolation problems with complete data 162
6.2 The associated Hermitian coupling matrix 167
6.3 J unitary on the imaginary axis with given null pole structure in the right
half plane 170
6.4 J unitary with poles on the imaginary axis 172
6.5 The case 3 = 1 175
7. Rational Matrix Functions with J Unitary Values on the Unit Circle 178
7.1 Realization theorems and examples 178
7.2 The associated Hermitian coupling matrix 185
7.3 J unitary on the unit circle with given null pole structure in the unit disk 186
7.4 J unitary with singularity at infinity 188
7.5 J unitary with poles on the unit circle 194
7.6 The case J = 1 197
Notes 199
PART II HOMOGENEOUS INTERPOLATION PROBLEMS WITH
OTHER FORMS OF LOCAL DATA
8. Interpolation Problems with Null and Pole Pairs 202
8.1 Rational matrix functions with given right null pairs and right pole pairs:
necessary conditions 202
8.2 Rational matrix functions with given right and left pole and null pairs 206
9. Interpolation Problems for Rational Matrix Functions Based on Divisibility 209
9.1 Statement of the problem and the main theorem 209
9.2 Proof of Theorem 9.1.1 211
9.3 A generalization 212
10. Polynomial Interpolation Problems Based on Divisibility 213
10.1 Divisibility of matrix polynomials 213
10.2 Least common multiples 219
11. Coprime Representations and an Interpolation Problem 224
11.1 Coprime matrix fractions 224
11.2 Local coprime matrix fractions 228
11.3 Rational matrix functions with given left numerator and right
denominator 230
11.4 Rational matrix functions with given numerator and
denominator from the opposite sides: local framework 234
Notes 235
CONTENTS
PART III SUBSPACE INTERPOLATION PROBLEMS
12. Null Pole Subspaces: Elementary Properties 237
12.1 Introduction and simple properties 237
12.2 Null pole subspace for an admissible data set 239
12.3 Null pole subspace from a null pole triple 251
12.4 Local null pole subspace in terms of Laurent coefficients 256
12.5 Local null pole subspace in terms of null and pole chains 260
13. Null Pole Subspaces for Matrix Functions with J Unitary Values on the
Imaginary Axis or Unit Circle 268
13.1 J unitary versus unitary matrix functions 268
13.2 Negative squares and null pole subspaces 273
14. Subspace Interpolation Problems 280
14.1 Interpolation of a given null pole subspace 280
14.2 A rational indefinite metric Beurling Lax theorem 285
14.3 A rational Ball Helton invariant subspace representation theory 290
15. Subspace Interpolation with Data at Infinity 293
15.1 Null pole subspace with data at infinity 293
15.2 Interpolation of a null pole subspace with data at infinity 298
15.3 A rational Ball Helton theorem: the general case 300
Notes 315
PART IV NONHOMOGENEOUS INTERPOLATION PROBLEMS
16. Interpolation Problems for Matrix Polynomials and Rational Matrix
Functions 317
16.1 Tangential Lagrange Sylvester interpolation 317
16.2 Lagrange Sylvester interpolation in contour integral form 321
16.3 Lagrange Sylvester interpolation in the divisor remainder form 328
16.4 Solutions of the one sided contour interpolation problem 329
16.5 Interpolation with several contour integral conditions 332
16.6 Interpolation of matrix polynomials with monic divisors and
the Vandermonde matrix 337
16.7 Interpolation of matrix polynomials with regular divisors 343
16.8 Two sided Lagrange Sylvester interpolation: introduction and examples 345
16.9 The two sided contour integral interpolation problem in the
divisor remainder form 352
16.10 Existence and linear fractional description of solutions of two sided
contour integral interpolation problem 357
16.11 The two sided contour integral interpolation problem with prescribed
number of poles 368
17. Partial Realization as an Interpolation Problem 371
17.1 Statement of the problem and introduction 371
17.2 Description of minimal partial realizations 372
17.3 Examples 376
Notes 379
CONTENTS
PART V NONHOMOGENEOUS INTERPOLATION PROBLEMS WITH
METRIC CONSTRAINTS
18. Matrix Nevanlinna Pick Interpolation and Generalizations 382
18.1 Classical Nevanlinna Pick interpolation 382
18.2 Tangential Nevanlinna Pick interpolation with simple multiplicities:
introduction and main result 383
18.3 Tangential Nevanlinna Pick interpolation with simple multiplicities:
proofs 390
18.4 Generalized Nevanlinna Pick interpolation: problem formulation 407
18.5 Solution of two sided Nudelman problem 409
18.6 Proofs of Theorems 18.6.1 and 18.6.2 417
19. Matrix Nevanlinna Pick Takagi Interpolation 425
19.1 Takagi Nudelman interpolation problem 425
19.2 Solution of the Takagi Nudelman interpolation problem: main results 428
19.3 Proofs of the main results 430
20. Nehari Interpolation Problem 434
20.1 The Nehari problem and the Hankel operator: the unit disk case 434
20.2 The Nehari problem and the Hankel operator: the half plane case 440
20.3 Solution of the Nehari problem 443
20.4 Proof of Theorem 20.3.2 446
20.5 The Nehari Takagi problem 452
21. Boundary Nevanlinna Pick Interpolation 457
21.1 Interpolation of angular derivatives: the scalar case 457
21.2 Tangential interpolation of matricial angular derivatives on the unit circle 463
21.3 Tangential interpolation of matricial angular derivatives on the imaginary
line 473
21.4 Solution of generalized angular derivative interpolation problem 478
22. Caratheodory Toeplitz Interpolation 487
22.1 The classical scalar case 487
22.2 Matrix Caratheodory Toeplitz interpolation problems 490
22.3 Proofs of the main results 493
Notes 500
PART VI SOME APPLICATIONS TO CONTROL AND SYSTEMS THEORY
23. Sensitivity Minimization 506
23.1 Engineering motivation 506
23.2 Interpolation characterization of stable sensitivities: the simple case 512
23.3 Interpolation characterization of stable sensitivities: the general case 516
23.4 Solution to the sensitivity minimization problem 520
23.5 Sensitivity minimization with weights 522
24. Model Reduction 533
24.1 Introduction 533
CONTENTS
24.2 The Hankel norm 534
24.3 Optimal Hankel norm model reduction 537
24.4 Discrete time systems 540
25. Robust Stabilizations 547
25.1 Introduction 547
25.2 Interpolation characterization of the Q parameter 552
25.3 Solution of the robust stabilization problem 557
Notes 560
APPENDIX. Sylvester, Lyapunov and Stein Equations 562
A.I Sylvester equations 562
A.2 Stein equations 569
A.3 Lyapunov and symmetric Stein equations 575
Notes 580
REFERENCES 581
NOTATIONS AND CONVENTIONS 595
INDEX 601
|
| any_adam_object | 1 |
| author | Ball, Joseph A. 1947- Gohberg, Yiśrāʿēl Z. 1928-2009 Rodman, Leiba 1949-2015 |
| author_GND | (DE-588)112083498 (DE-588)118915878 (DE-588)130488631 |
| author_facet | Ball, Joseph A. 1947- Gohberg, Yiśrāʿēl Z. 1928-2009 Rodman, Leiba 1949-2015 |
| author_role | aut aut aut |
| author_sort | Ball, Joseph A. 1947- |
| author_variant | j a b ja jab y z g yz yzg l r lr |
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| dewey-full | 515/.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.73 |
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| dewey-sort | 3515 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV002727387 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:48:47Z |
| institution | BVB |
| isbn | 3764324767 0817624767 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001747175 |
| oclc_num | 21521892 |
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| physical | 605 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Ball, Joseph A. 1947- Verfasser (DE-588)112083498 aut Interpolation of rational matrix functions Joseph A. Ball ; Israel Gohberg ; Leiba Rodman Basel u.a. Birkhäuser 1990 605 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 45 Espaces d'interpolation ram Interpolatie gtt Matrices gtt Matrices ram fonction matricielle fonction rationnelle interpolation théorie interpolation théorie opérateur théorie système Interpolation spaces Matrices Operatortheorie (DE-588)4075665-8 gnd rswk-swf Rationale matrixwertige Funktion (DE-588)4201287-9 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Rationale matrixwertige Funktion (DE-588)4201287-9 s Interpolation (DE-588)4162121-9 s DE-604 Operatortheorie (DE-588)4075665-8 s Gohberg, Yiśrāʿēl Z. 1928-2009 Verfasser (DE-588)118915878 aut Rodman, Leiba 1949-2015 Verfasser (DE-588)130488631 aut Operator theory 45 (DE-604)BV000000970 45 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001747175&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ball, Joseph A. 1947- Gohberg, Yiśrāʿēl Z. 1928-2009 Rodman, Leiba 1949-2015 Interpolation of rational matrix functions Operator theory Espaces d'interpolation ram Interpolatie gtt Matrices gtt Matrices ram fonction matricielle fonction rationnelle interpolation théorie interpolation théorie opérateur théorie système Interpolation spaces Matrices Operatortheorie (DE-588)4075665-8 gnd Rationale matrixwertige Funktion (DE-588)4201287-9 gnd Interpolation (DE-588)4162121-9 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)4201287-9 (DE-588)4162121-9 |
| title | Interpolation of rational matrix functions |
| title_auth | Interpolation of rational matrix functions |
| title_exact_search | Interpolation of rational matrix functions |
| title_full | Interpolation of rational matrix functions Joseph A. Ball ; Israel Gohberg ; Leiba Rodman |
| title_fullStr | Interpolation of rational matrix functions Joseph A. Ball ; Israel Gohberg ; Leiba Rodman |
| title_full_unstemmed | Interpolation of rational matrix functions Joseph A. Ball ; Israel Gohberg ; Leiba Rodman |
| title_short | Interpolation of rational matrix functions |
| title_sort | interpolation of rational matrix functions |
| topic | Espaces d'interpolation ram Interpolatie gtt Matrices gtt Matrices ram fonction matricielle fonction rationnelle interpolation théorie interpolation théorie opérateur théorie système Interpolation spaces Matrices Operatortheorie (DE-588)4075665-8 gnd Rationale matrixwertige Funktion (DE-588)4201287-9 gnd Interpolation (DE-588)4162121-9 gnd |
| topic_facet | Espaces d'interpolation Interpolatie Matrices fonction matricielle fonction rationnelle interpolation théorie interpolation théorie opérateur théorie système Interpolation spaces Operatortheorie Rationale matrixwertige Funktion Interpolation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001747175&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT balljosepha interpolationofrationalmatrixfunctions AT gohbergyisraʿelz interpolationofrationalmatrixfunctions AT rodmanleiba interpolationofrationalmatrixfunctions |