Factorization of matrix and operator functions: the state space method
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel <<[u.a.]>>
Birkhäuser
2007
|
| Schriftenreihe: | Operator theory
178 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 409 S. |
| ISBN: | 9783764382674 3764382678 |
Internformat
MARC
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| 245 | 1 | 0 | |a Factorization of matrix and operator functions |b the state space method |c Harm Bart ... |
| 264 | 1 | |a Basel <<[u.a.]>> |b Birkhäuser |c 2007 | |
| 300 | |a XII, 409 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 178 | |
| 650 | 0 | 7 | |a Faktorisierung |0 (DE-588)4128927-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Operatorfunktion |0 (DE-588)4202830-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zustandsraum |0 (DE-588)4132647-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Faktorisierung |0 (DE-588)4128927-4 |D s |
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| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Operatorfunktion |0 (DE-588)4202830-9 |D s |
| 689 | 1 | 1 | |a Faktorisierung |0 (DE-588)4128927-4 |D s |
| 689 | 1 | 2 | |a Zustandsraum |0 (DE-588)4132647-7 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Bart, Harm |d 1942- |0 (DE-588)109309847 |4 edt | |
| 830 | 0 | |a Operator theory |v 178 |w (DE-604)BV000000970 |9 178 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018589490&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018589490 | ||
Datensatz im Suchindex
| _version_ | 1804140636279930880 |
|---|---|
| adam_text | CONTENTS
PREFACE
...................................... X
I
0 INTRODUCTION
................................. 1
PART I MOTIVATING PROBLEMS, SYSTEMS AND REALIZATIONS
1 MOTIVATING PROBLEMS
1.1 LINEAR TIME INVARIANT SYSTEMS AND CASCADE CONNECTION . . . . . . . 7
1.2 CHARACTERISTIC OPERATOR FUNCTIONS AND INVARIANT SUBSPACES (1) . . .
11
1.3 CHARACTERISTIC OPERATOR FUNCTIONS AND INVARIANT SUBSPACES (2) . . .
14
1.4 FACTORIZATION OF MONIC MATRIX POLYNOMIALS . . . . . . . . . . . . .
. 17
1.5 WIENER-HOPF INTEGRAL OPERATORS AND FACTORIZATION . . . . . . . . . .
18
1.6 BLOCK TOEPLITZ EQUATIONS AND FACTORIZATION . . . . . . . . . . . . .
. 21
NO
T
E
S .................................. 2
3
2 OPERATOR NODES, SYSTEMS, AND OPERATIONS ON SYSTEMS
2.1 OPERATOR NODES, SYSTEMS AND TRANSFER FUNCTIONS . . . . . . . . . . .
25
2
.
2 I
N
V
E
R
S
I
O
N................................. 2
7
2
.
3 PR
O
D
U
C
T
S................................. 3
0
2.4 FACTORIZATION AND MATCHING OF INVARIANT SUBSPACES . . . . . . . . .
32
2.5 FACTORIZATION AND INVERSION REVISITED . . . . . . . . . . . . . . .
. . 37
NO
T
E
S .................................. 4
8
3 VARIOUS CLASSES OF SYSTEMS
3
.
1 BR
O
D
S
K
I
IS
Y
S
T
E
MS ............................ 4
9
3.2 KRE**
NSY
S
T
E
MS.............................. 5
0
3
.
3 UN
I
T
A
R
YSY
S
T
E
MS ............................ 5
1
3
.
4 MO
N
I
CSY
S
T
E
MS ............................. 5
3
3
.
5 PO
L
Y
N
O
MI
A
LS
Y
S
T
E
MS........................... 5
7
3.6 M¨O
B
I
U
ST
R
A
N
S
F
O
R
MA
T
I
O
NOFS
Y
S
T
E
MS .................. 5
8
NO
T
E
S .................................. 6
4
VIII CONTENTS
4 REALIZATION
AND LINEARIZATION
OF
OPERATOR
FUNCTIONS
4.1 REALIZATION OF RATIONAL OPERATOR FUNCTIONS . . . . . . . . . . . . .
. 65
4
.
2 RE
A
L
I
Z
A
T
I
O
NOFA
N
A
L
Y
T
I
COP
E
R
A
T
O
RF
U
N
C
T
I
O
N
S .............. 6
7
4
.
3 LI
N
E
A
R
I
Z
A
T
I
O
N .............................. 6
9
4.4 LINEARIZATION AND SCHUR COMPLEMENTS . . . . . . . . . . . . . . . .
73
NO
T
E
S .................................. 7
6
5 FACTORIZATION AND RICCATI EQUATIONS
5.1 ANGULAR SUBSPACES AND ANGULAR OPERATORS . . . . . . . . . . . . . .
77
5.2 ANGULAR SUBSPACES AND THE ALGEBRAIC RICCATI EQUATION . . . . . . .
79
5.3 ANGULAR OPERATORS AND FACTORIZATION . . . . . . . . . . . . . . . .
. 80
5.4 ANGULAR SPECTRAL SUBSPACES AND THE ALGEBRAIC RICCATI EQUATION . . .
86
NO
T
E
S .................................. 8
8
6 CANONICAL FACTORIZATION AND APPLICATIONS
6.1 CANONICAL FACTORIZATION OF RATIONAL MATRIX FUNCTIONS . . . . . . . .
. 89
6.2 APPLICATION TO WIENER-HOPF INTEGRAL EQUATIONS . . . . . . . . . . .
92
6
.
3 AP
P
L
I
C
A
T
I
O
NTOBL
O
C
KTO
E
P
L
I
T
ZOPE
R
A
T
O
R
S ............... 9
7
NO
T
E
S .................................. 1
0
0
PART II MINIMAL REALIZATION AND MINIMAL FACTORIZATION
7 MINIMAL SYSTEMS
7
.
1 MI
N
I
MA
L
I
T
YOFS
Y
S
T
E
MS ......................... 1
0
5
7.2 CONTROLLABILITY AND OBSERVABILITY FOR FINITE-DIMENSIONAL SYSTEMS . .
109
7.3 MINIMALITY FOR FINITE-DIMENSIONAL SYSTEMS . . . . . . . . . . . . .
. 112
7.4 MINIMALITY FOR HILBERT SPACE SYSTEMS . . . . . . . . . . . . . . . .
. 116
7
.
5 MI
N
I
MA
L
I
T
YI
NSPE
C
I
A
LC
A
S
E
S....................... 1
2
5
7
.
5
.
1 BR
O
D
S
K
I
IS
Y
S
T
E
MS........................ 1
2
5
7.5.2 KRE**
NSY
S
T
E
MS.......................... 1
2
5
7
.
5
.
3 UN
I
T
A
R
YSY
S
T
E
MS ........................ 1
2
6
7
.
5
.
4 MO
N
I
CSY
S
T
E
MS ......................... 1
2
7
7.5.5 POLYNOMIAL SYSTEMS . . . . . . . . . . . . . . . . . . . . . . 128
NO
T
E
S .................................. 1
2
8
8 MINIMAL REALIZATIONS AND POLE-ZERO STRUCTURE
8
.
1 ZE
R
ODA
T
AAN
DJO
R
D
A
NCH
A
I
N
S ..................... 1
2
9
8
.
2 PO
L
EDA
T
A ................................ 1
4
2
8.3 MINIMAL REALIZATIONS IN TERMS OF ZERO OR POLE DATA . . . . . . . . .
. 145
8.4 LOCAL DEGREE AND LOCAL MINIMALITY . . . . . . . . . . . . . . . . .
. . 147
8.5 MCMILLAN DEGREE AND MINIMALITY OF SYSTEMS . . . . . . . . . . . . .
160
NO
T
E
S .................................. 1
6
1
CONTENTS IX
9 MINIMAL
FACTORIZATION
OF
RATIONAL
MATRIX
FUNCTIONS
9
.
1 MI
N
I
MA
LF
A
C
T
O
R
I
Z
A
T
I
O
N ......................... 1
6
3
9
.
2 PS
E
U
D
O
-
C
A
N
O
N
I
C
A
LF
A
C
T
O
R
I
Z
A
T
I
O
N .................... 1
6
9
9.3 MINIMAL FACTORIZATION IN A SINGULAR CASE . . . . . . . . . . . . . .
. 172
NO
T
E
S .................................. 1
7
9
PART III DEGREE ONE FACTORS, COMPANION BASED RATIONAL
MATRIX FUNCTIONS, AND JOB SCHEDULING
10 FACTORIZATION INTO DEGREE ONE FACTORS
10.1 SIMULTANEOUS REDUCTION TO COMPLEMENTARY TRIANGULAR FORMS . . . .
184
10.2 FACTORIZATION INTO ELEMENTARY FACTORS AND REALIZATION . . . . . . .
. 188
10.3 COMPLETE FACTORIZATION (GENERAL) . . . . . . . . . . . . . . . . .
. . 195
10.4 QUASICOMPLETE FACTORIZATION (GENERAL) . . . . . . . . . . . . . . .
. 199
NO
T
E
S .................................. 2
0
9
11 COMPLETE FACTORIZATION OF COMPANION BASED MATRIX FUNCTIONS
11.1 COMPANION MATRICES: PRELIMINARIES . . . . . . . . . . . . . . . . .
. 212
11.2 SIMULTANEOUS REDUCTION TO COMPLEMENTARY TRIANGULAR FORMS . . . .
216
11.3 PRELIMINARIES ABOUT COMPANION BASED MATRIX FUNCTIONS . . . . . . .
231
11.4 COMPANION BASED MATRIX FUNCTIONS: POLES AND ZEROS . . . . . . . . .
234
11.5 COMPLETE FACTORIZATION (COMPANION BASED) . . . . . . . . . . . . .
. 244
11.6 MAPLE PROCEDURES FOR CALCULATING COMPLETE FACTORIZATIONS . . . . .
. 246
11.6.1 MAPLE ENVIRONMENT AND PROCEDURES . . . . . . . . . . . . . . 247
11.6.2 POLES, ZEROS AND ORDERINGS . . . . . . . . . . . . . . . . . . .
247
11.6.3 TRIANGULARIZATION ROUTINES (COMPLETE) . . . . . . . . . . . . 251
11.6.4 FACTORIZATION PROCEDURES . . . . . . . . . . . . . . . . . . . .
252
1
1
.
6
.
5EX
A
MP
L
E............................. 2
5
4
11.7 APPENDIX: INVARIANT SUBSPACES OF COMPANION MATRICES . . . . . . .
260
NO
T
E
S .................................. 2
6
6
12 QUASICOMPLETE FACTORIZATION AND JOB SCHEDULING
1
2
.
1ACO
MB
I
N
A
T
O
R
I
A
LL
E
MMA ........................ 2
6
8
12.2 QUASICOMPLETE FACTORIZATION (COMPANION BASED) . . . . . . . . . . .
272
12.3 A REVIEW OF THE TWO MACHINE FLOW SHOP PROBLEM . . . . . . . . . . .
288
12.4 QUASICOMPLETE FACTORIZATION AND THE 2MSFP . . . . . . . . . . . . .
293
12.5 MAPLE PROCEDURES FOR QUASICOMPLETE FACTORIZATIONS . . . . . . . . .
301
1
2
.
5
.
1MA
P
L
EEN
V
I
R
O
N
ME
N
T....................... 3
0
2
12.5.2 TRIANGULARIZATION ROUTINES (QUASICOMPLETE) . . . . . . . . . 303
12.5.3 TRANSFORMATIONS INTO UPPER TRIANGULAR FORM . . . . . . . . . 307
12.5.4 TRANSFORMATION INTO COMPLEMENTARY TRIANGULAR FORMS . . . 308
X CONTENTS
12.5.5 AN EXAMPLE: SYMBOLIC AND QUASICOMPLETE . . . . . . . . . . 309
1
2
.
5
.
6CO
N
C
L
U
D
I
N
GRE
MA
R
K
S ...................... 3
1
4
NO
T
E
S .................................. 3
1
5
PART IV STABILITY OF FACTORIZATION AND OF INVARIANT SUBSPACES
13 STABILITY OF SPECTRAL DIVISORS
13.1 EXAMPLES AND FIRST RESULTS FOR THE FINITE-DIMENSIONAL CASE . . . .
. . 319
13.2 OPENING BETWEEN SUBSPACES AND ANGULAR OPERATORS . . . . . . . . .
322
13.3 STABILITY OF SPECTRAL DIVISORS OF SYSTEMS . . . . . . . . . . . . .
. . . 327
13.4 APPLICATIONS TO TRANSFER FUNCTIONS . . . . . . . . . . . . . . . .
. . . 332
1
3
.
5AP
P
L
I
C
A
T
I
O
N
ST
ORI
C
C
A
T
IE
Q
U
A
T
I
O
N
S................... 3
3
5
NO
T
E
S .................................. 3
3
8
14 STABILITY OF DIVISORS
1
4
.
1ST
A
B
L
EI
N
V
A
R
I
A
N
TS
U
B
S
P
A
C
E
S....................... 3
3
9
14.2 LIPSCHITZ STABLE INVARIANT SUBSPACES . . . . . . . . . . . . . . .
. . . 345
14.3 STABLE MINIMAL FACTORIZATIONS OF RATIONAL MATRIX FUNCTIONS . . . .
. 348
14.4 STABLE COMPLETE FACTORIZATIONS . . . . . . . . . . . . . . . . . .
. . . 352
14.5 STABLE FACTORIZATIONS OF MONIC MATRIX POLYNOMIALS . . . . . . . . .
. 356
14.6 STABLE SOLUTIONS OF THE OPERATOR RICCATI EQUATION . . . . . . . . .
. 359
14.7 STABILITY OF STABLE FACTORIZATIONS . . . . . . . . . . . . . . . .
. . . . 360
14.8 ISOLATED FACTORIZATIONS AND RELATED TOPICS . . . . . . . . . . . .
. . . 363
14.8.1 ISOLATED INVARIANT SUBSPACES . . . . . . . . . . . . . . . . . .
363
14.8.2 ISOLATED CHAINS OF INVARIANT SUBSPACES . . . . . . . . . . . .
366
14.8.3 ISOLATED FACTORIZATIONS . . . . . . . . . . . . . . . . . . . . .
369
14.8.4 ISOLATED SOLUTIONS OF THE RICCATI EQUATION . . . . . . . . . .
372
NO
T
E
S .................................. 3
7
2
15 FACTORIZATION OF REAL MATRIX FUNCTIONS
1
5
.
1RE
A
LMA
T
R
I
XF
U
N
C
T
I
O
N
S ......................... 3
7
5
15.2 REAL MONIC MATRIX POLYNOMIALS . . . . . . . . . . . . . . . . . . .
. 378
15.3 STABLE AND ISOLATED INVARIANT SUBSPACES . . . . . . . . . . . . . .
. . 379
15.4 STABLE AND ISOLATED REAL FACTORIZATIONS . . . . . . . . . . . . . .
. . 385
15.5 STABILITY OF STABLE REAL FACTORIZATIONS . . . . . . . . . . . . . .
. . . 389
NO
T
E
S .................................. 3
9
1
BIBLIOGRAPHY
................................... 3
9
3
LIST OF SYMBOLS
.................................. 4
0
1
INDEX
....................................... 4
0
5
|
| any_adam_object | 1 |
| author2 | Bart, Harm 1942- |
| author2_role | edt |
| author2_variant | h b hb |
| author_GND | (DE-588)109309847 |
| author_facet | Bart, Harm 1942- |
| building | Verbundindex |
| bvnumber | BV024617269 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)916652313 (DE-599)DNB983609594 |
| dewey-full | 515.724 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.724 |
| dewey-search | 515.724 |
| dewey-sort | 3515.724 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV024617269 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:03:07Z |
| institution | BVB |
| isbn | 9783764382674 3764382678 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018589490 |
| oclc_num | 916652313 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | XII, 409 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Factorization of matrix and operator functions the state space method Harm Bart ... Basel <<[u.a.]>> Birkhäuser 2007 XII, 409 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 178 Faktorisierung (DE-588)4128927-4 gnd rswk-swf Operatorfunktion (DE-588)4202830-9 gnd rswk-swf Zustandsraum (DE-588)4132647-7 gnd rswk-swf Matrixfunktion (DE-588)4169117-9 gnd rswk-swf Matrixfunktion (DE-588)4169117-9 s Faktorisierung (DE-588)4128927-4 s Zustandsraum (DE-588)4132647-7 s DE-604 Operatorfunktion (DE-588)4202830-9 s Bart, Harm 1942- (DE-588)109309847 edt Operator theory 178 (DE-604)BV000000970 178 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018589490&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Factorization of matrix and operator functions the state space method Operator theory Faktorisierung (DE-588)4128927-4 gnd Operatorfunktion (DE-588)4202830-9 gnd Zustandsraum (DE-588)4132647-7 gnd Matrixfunktion (DE-588)4169117-9 gnd |
| subject_GND | (DE-588)4128927-4 (DE-588)4202830-9 (DE-588)4132647-7 (DE-588)4169117-9 |
| title | Factorization of matrix and operator functions the state space method |
| title_auth | Factorization of matrix and operator functions the state space method |
| title_exact_search | Factorization of matrix and operator functions the state space method |
| title_full | Factorization of matrix and operator functions the state space method Harm Bart ... |
| title_fullStr | Factorization of matrix and operator functions the state space method Harm Bart ... |
| title_full_unstemmed | Factorization of matrix and operator functions the state space method Harm Bart ... |
| title_short | Factorization of matrix and operator functions |
| title_sort | factorization of matrix and operator functions the state space method |
| title_sub | the state space method |
| topic | Faktorisierung (DE-588)4128927-4 gnd Operatorfunktion (DE-588)4202830-9 gnd Zustandsraum (DE-588)4132647-7 gnd Matrixfunktion (DE-588)4169117-9 gnd |
| topic_facet | Faktorisierung Operatorfunktion Zustandsraum Matrixfunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018589490&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT bartharm factorizationofmatrixandoperatorfunctionsthestatespacemethod |