Selected problems of fractional systems theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Lecture notes in control and information sciences
411 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XVII, 344 S. graph. Darst. 23 cm |
| ISBN: | 9783642205019 3642205011 |
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Record in the Search Index
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IMAGE 1
CONTENTS
PREFACE V
LIST OF SYMBOLS IX
LIST OF FIGURES XI
1 FRACTIONAL DISCRETE-TIME LINEAR SYSTEMS 1
1.1 DEFINITION OF N-ORDER DIFFERENCE 1
1.2 STATE EQUATIONS OF THE FRACTIONAL LINEAR SYSTEMS 2
1.2.1 FRACTIONAL SYSTEMS WITHOUT DELAYS 2
1.2.2 FRACTIONAL SYSTEMS WITH DELAYS 3
1.3 SOLUTION OF THE STATE EQUATIONS OF THE FRACTIONAL DISCRETE-TIME
LINEAR SYSTEM WITH DELAYS 4
1.3.1 FRACTIONAL SYSTEMS WITH DELAYS 4
1.3.2 FRACTIONAL SYSTEMS WITHOUT DELAYS 6
1.4 POSITIVE FRACTIONAL LINEAR SYSTEMS 7
1.5 EXTERNALLY POSITIVE FRACTIONAL SYSTEMS 9
1.6 REACHABILITY OF FRACTIONAL DISCRETE-TIME LINEAR SYSTEMS 10 1.7
REACHABILITY OF POSITIVE FRACTIONAL DISCRETE-TIME LINEAR SYSTEMS 12
1.8 CONTROLLABILITY TO ZERO OF THE FRACTIONAL DISCRETE-TIME LINEAR
SYSTEMS 15
1.9 CONTROLLABILITY TO ZERO OF POSITIVE FRACTIONAL DISCRETE-TIME LINEAR
SYSTEMS 18
1.10 MINIMUM ENERGY CONTROL OF POSITIVE FRACTIONAL SYSTEMS 19 1.11
FRACTIONAL DIFFERENT ORDERS DISCRETE-TIME LINEAR SYSTEMS 22 1.12
POSITIVE FRACTIONAL DIFFERENT ORDERS DISCRETE-TIME LINEAR SYSTEMS 24
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/101060225X
DIGITALISIERT DURCH
IMAGE 2
XIV CONTENTS
2 FRACTIONAL CONTINUOUS-TIME LINEAR SYSTEMS 27
2.1 DEFINITION OF EULER GAMMA FUNCTION AND ITS PROPERTIES 27 2.2
MITTAG-LEFFLER FUNCTION 28
2.3 DEFINITIONS OF FRACTIONAL DERIVATIVE-INTEGRAL 28
2.3.1 RIEMANN-LIOUVILLE DEFINITION 28
2.3.2 CAPUTO DEFINITION 30
2.4 SOLUTION OF THE FRACTIONAL STATE EQUATION OF CONTINUOUS-TIME LINEAR
SYSTEM 31
2.5 POSITIVITY OF THE FRACTIONAL SYSTEMS 35
2.6 EXTERNAL POSITIVITY OF THE FRACTIONAL SYSTEMS 36
2.7 REACHABILITY OF FRACTIONAL POSITIVE CONTINUOUS-TIME LINEAR SYSTEM 37
2.8 POSITIVE CONTINUOUS-TIME LINEAR SYSTEMS WITH DELAYS 40 2.9 POSITIVE
LINEAR SYSTEMS CONSISTING OF N SUBSYSTEMS WITH DIFFERENT FRACTIONAL
ORDERS 42
2.9.1 LINEAR DIFFERENTIAL EQUATIONS WITH DIFFERENT FRACTIONAL ORDERS 42
2.9.2 POSITIVE FRACTIONAL SYSTEMS 46
2.9.3 FRACTIONAL LINEAR ELECTRICAL CIRCUITS 47
3 FRACTIONAL POSITIVE 2D LINEAR SYSTEMS 53
3. 1 DEFINITION OF (BACKWARD) FRACTIONAL DIFFERENCE OF 2D FUNCTION . .
53 3.2 STATE EQUATION OF FRACTIONAL 2D LINEAR SYSTEMS 53
3.3 SOLUTION OF THE STATE EQUATION OF THE FRACTIONAL 2D LINEAR SYSTEM 54
3.4 EXTENSION OF THE CAYLEY-HAMILTON THEOREM 56
3.5 POSITIVITY OF FRACTIONAL 2D LINEAR SYSTEMS 57
3.6 REACHABILITY AND CONTROLLABILITY OF POSITIVE FRACTIONAL 2D LINEAR
SYSTEMS 58
3.7 CONTROLLABILITY TO ZERO OF POSITIVE FRACTIONAL 2D LINEAR SYSTEM.
61 3.8 MODELS OF 2D LINEAR SYSTEMS 62
3.8.1 POSITIVE 2D LINEAR SYSTEMS 62
3.8.2 POSITIVE FRACTIONAL 2D LINEAR SYSTEMS 63
3.8.3 POSITIVE 2D LINEAR SYSTEMS WITH DELAYS 69
3.9 POSITIVE FRACTIONAL 2D LINEAR SYSTEM OF DIFFERENT ORDERS 71 3.9.1
DEFINITION OF (BACKWARD) DIFFERENCE OF (A, SS) ORDER OF 2D FUNCTION 71
3.9.2 STATE EQUATIONS OF FRACTIONAL 2D LINEAR SYSTEM 71 3.9.3 SOLUTION
OF THE STATE EQUATIONS OF THE FRACTIONAL 2D LINEAR SYSTEMS 72
3.9.4 EXTENSION OF THE CAYLEY-HAMILTON THEOREM 77
3.9.5 POSITIVITY OF THE FRACTIONAL 2D LINEAR SYSTEMS 78
IMAGE 3
CONTENTS XV
4 POINTWISE COMPLETENESS AND POINTWISE DEGENERACY OF LINEAR SYSTEMS 81
4.1 STANDARD DISCRETE-TIME LINEAR SYSTEMS 81
4.2 STANDARD CONTINUOUS-TIME LINEAR SYSTEMS 82
4.3 STANDARD DISCRETE-TIME LINEAR SYSTEMS WITH DELAYS 83 4.4 POSITIVE
DISCRETE-TIME LINEAR SYSTEMS 84
4.5 POSITIVE CONTINUOUS-TIME LINEAR SYSTEMS 85
4.6 POSITIVE DISCRETE-TIME LINEAR SYSTEMS WITH DELAYS 86
4.7 FRACTIONAL DISCRETE-TIME LINEAR SYSTEMS 88
4.8 FRACTIONAL CONTINUOUS-TIME LINEAR SYSTEMS 89
4.9 POSITIVE FRACTIONAL DISCRETE-TIME LINEAR SYSTEM 92
4.10 POSITIVE FRACTIONAL CONTINUOUS-TIME LINEAR SYSTEMS 93 4.11
POINTWISE COMPLETENESS AND POINTWISE DEGENERACY OF ELECTRICAL CIRCUITS
94
4.12 STANDARD CONTINUOUS-DISCRETE LINEAR SYSTEM DESCRIBED BY THE GENERAL
MODEL 96
4.13 POSITIVE CONTINUOUS-DISCRETE LINEAR SYSTEM DESCRIBED BY THE GENERAL
MODEL 99
5 POINTWISE COMPLETENESS AND POINTWISE DEGENERACY OF LINEAR SYSTEMS WITH
STATE-FEEDBACKS 103
5.1 STANDARD DISCRETE-TIME LINEAR SYSTEMS 103
5.2 STANDARD CONTINUOUS-TIME LINEAR SYSTEMS 108
5.3 POSITIVE STANDARD DISCRETE-TIME LINEAR SYSTEMS 108
5.4 POSITIVE STANDARD CONTINUOUS-TIME LINEAR SYSTEMS I LL
5.5 FRACTIONAL DISCRETE-TIME LINEAR SYSTEMS 114
5.6 FRACTIONAL CONTINUOUS-TIME LINEAR SYSTEMS 114
5.7 POSITIVE FRACTIONAL DISCRETE-TIME LINEAR SYSTEM 115
5.8 POSITIVE FRACTIONAL CONTINUOUS-TIME LINEAR SYSTEMS 116
6 REALIZATION PROBLEM FOR POSITIVE FRACTIONAL AND CONTINUOUS-DISCRETE 2D
LINEAR SYSTEMS 117
6.1 FRACTIONAL DISCRETE-TIME LINEAR SYSTEMS 117
6.1.1 SISO SYSTEMS 119
6.1.2 MIMO SYSTEMS 123
6.2 FRACTIONAL CONTINUOUS-TIME LINEAR SYSTEMS 130
6.2.1 SISO SYSTEMS 131
6.2.2 MIMO SYSTEMS 133
7 CONE DISCRETE-TIME AND CONTINUOUS-TIME LINEAR SYSTEMS 141 7.1 BASIC
DEFINITIONS 141
7.1.1 CONE DISCRETE-TIME SYSTEMS 141
7.1.2 CONE CONTINUOUS-TIME SYSTEMS WITH DELAYS 142 7.1.3 CONE FRACTIONAL
DISCRETE-TIME SYSTEMS 144
7.1.4 CONE FRACTIONAL CONTINUOUS-TIME SYSTEM 145
IMAGE 4
XVI CONTENTS
7.2 REACHABILITY OF CONE FRACTIONAL SYSTEMS 146
7.2.1 CONE FRACTIONAL DISCRETE-TIME SYSTEMS 146
7.2.2 CONE FRACTIONAL CONTINUOUS-TIME SYSTEM 148
7.3 CONTROLLABILITY TO ZERO OF CONE FRACTIONAL DISCRETE-TIME SYSTEMS 149
7.4 CONE REALIZATION PROBLEM FOR LINEAR SYSTEMS 150
7.4.1 DISCRETE-TIME LINEAR SYSTEMS 150
7.4.2 CONE REALIZATION PROBLEM FOR CONTINUOUS-TIME SYSTEMS WITH DELAYS
153
8 STABILITY OF POSITIVE FRACTIONAL ID AND 2D LINEAR SYSTEMS 161 8.1
ASYMPTOTIC STABILITY OF DISCRETE-TIME LINEAR SYSTEMS 161 8.1.1 POSITIVE
DISCRETE-TIME SYSTEMS 161
8.1.2 POSITIVE 2D LINEAR SYSTEMS 165
8.1.3 RELATIONSHIP BETWEEN ASYMPTOTIC STABILITY OF ID AND 2D LINEAR
SYSTEMS 168
8.1.4 POSITIVE FRACTIONAL DISCRETE-TIME LINEAR SYSTEMS WITH DELAYS 171
8.1.5 POSITIVE FRACTIONAL 2D LINEAR SYSTEMS 173
8.2 PRACTICAL STABILITY OF FRACTIONAL SYSTEMS 176
8.2.1 POSITIVE FRACTIONAL ID SYSTEMS 176
8.2.2 POSITIVE FRACTIONAL 2D SYSTEMS 180
8.3 ASYMPTOTIC STABILITY OF CONTINUOUS-TIME LINEAR SYSTEMS 182 8.3.1
POSITIVE CONTINUOUS-TIME LINEAR SYSTEMS 182
8.3.2 ASYMPTOTIC STABILITY OF POSITIVE CONTINUOUS-TIME SYSTEMS WITH
DELAYS 185
9 STABILITY ANALYSIS OF FRACTIONAL LINEAR SYSTEMS IN FREQUENCY DOMAIN
189
9. 1 FRACTIONAL CONTINUOUS-TIME SYSTEMS 189
9.2 FRACTIONAL CONTINUOUS-TIME SYSTEMS WITH DELAYS OF THE RETARDED TYPE
198
9.3 FRACTIONAL DISCRETE-TIME SYSTEMS 205
9.4 ROBUST STABILITY OF CONVEX COMBINATION OF TWO FRACTIONAL POLYNOMIALS
211
10 STABILIZATION OF POSITIVE AND FRACTIONAL LINEAR SYSTEMS 221 10.1
FRACTIONAL DISCRETE-TIME LINEAR SYSTEMS WITH DELAYS 221 10.2 FRACTIONAL
CONTINUOUS-TIME LINEAR SYSTEMS WITH DELAYS 224 10.3 APPLICATION OF LMI
TO STABILIZATION OF FRACTIONAL LINEAR
SYSTEMS 227
10.3.1 FRACTIONAL ID LINEAR SYSTEMS 227
10.3.2 POSITIVE 2D LINEAR SYSTEMS 231
10.3.3 POSITIVE 2D LINEAR SYSTEMS WITH DELAYS 233
10.3.4 FRACTIONAL 2D ROESSER MODEL 238
IMAGE 5
CONTENTS XVII
11 SINGULAR FRACTIONAL LINEAR SYSTEMS 245
11.1 SINGULAR FRACTIONAL CONTINUOUS-TIME LINEAR SYSTEMS 245 11.2
SINGULAR FRACTIONAL ELECTRICAL CIRCUITS 247
11.3 SINGULAR FRACTIONAL DISCRETE-TIME LINEAR SYSTEMS 251 11.4 REDUCTION
OF SINGULAR FRACTIONAL SYSTEMS TO EQUIVALENT STANDARD FRACTIONAL SYSTEMS
258
11.5 DECOMPOSITION OF SINGULAR FRACTIONAL SYSTEM INTO DYNAMIC AND STATIC
PARTS 263
12 POSITIVE CONTINUOUS-DISCRETE LINEAR SYSTEMS 267
12.1 GENERAL MODEL OF CONTINUOUS-DISCRETE LINEAR SYSTEMS AND ITS
SOLUTION 267
12.2 POSITIVE GENERAL MODEL OF CONTINUOUS-DISCRETE LINEAR SYSTEMS 269
12.3 REACHABILITY OF THE STANDARD AND POSITIVE GENERAL MODEL 272 12.4
STABILITY OF THE POSITIVE GENERAL MODEL 278
12.5 ROBUST STABILITY OF LINEAR CONTINUOUS-DISCRETE LINEAR SYSTEM 286
12.6 POSITIVE REALIZATION PROBLEM FOR CONTINUOUS-DISCRETE LINEAR SYSTEMS
292
12.6.1 PROBLEM FORMULATION 292
12.6.2 SISO SYSTEMS 294
12.6.3 MIMO SYSTEMS 301
A LAPLACE TRANSFORMS OF CONTINUOUS-TIME FUNCTIONS AND Z-TRANSFORMS OF
DISCRETE-TIME FUNCTIONS 307
A. 1 CONVOLUTIONS OF CONTINUOUS-TIME AND DISCRETE-TIME FUNCTIONS AND
THEIR TRANSFORMS 307
A.2 LAPLACE TRANSFORMS OF DERIVATIVE-INTEGRALS 308
A.3 Z-TRANSFORMS OF DISCRETE-TIME FUNCTIONS 309
B INFINITE LONG CABLE WITH ZERO INDUCTANCE AS AN EXAMPLE OF
FRACTIONAL SYSTEM 313
C RIGHT INVERSE OF MATRICES 317
D ELEMENTARY OPERATIONS ON MATRICES 321
REFERENCES 323
INDEX 341 |
| any_adam_object | 1 |
| author | Kaczorek, Tadeusz 1932- |
| author_GND | (DE-588)110868889 |
| author_facet | Kaczorek, Tadeusz 1932- |
| author_role | aut |
| author_sort | Kaczorek, Tadeusz 1932- |
| author_variant | t k tk |
| building | Verbundindex |
| bvnumber | BV039117625 |
| classification_rvk | SI 845 |
| ctrlnum | (OCoLC)725022520 (DE-599)DNB101060225X |
| dewey-full | 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.39 |
| dewey-search | 515.39 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV039117625 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T11:13:24Z |
| institution | BVB |
| isbn | 9783642205019 3642205011 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024136257 |
| oclc_num | 725022520 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | XVII, 344 S. graph. Darst. 23 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Kaczorek, Tadeusz 1932- Verfasser (DE-588)110868889 aut Selected problems of fractional systems theory Tadeusz Kaczorek Berlin [u.a.] Springer 2011 XVII, 344 S. graph. Darst. 23 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 411 Literaturangaben Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Positives System (DE-588)4746300-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Positives System (DE-588)4746300-4 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Lecture notes in control and information sciences 411 (DE-604)BV005848579 411 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3702271&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024136257&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaczorek, Tadeusz 1932- Selected problems of fractional systems theory Lecture notes in control and information sciences Kontrolltheorie (DE-588)4032317-1 gnd Dynamisches System (DE-588)4013396-5 gnd Positives System (DE-588)4746300-4 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4013396-5 (DE-588)4746300-4 |
| title | Selected problems of fractional systems theory |
| title_auth | Selected problems of fractional systems theory |
| title_exact_search | Selected problems of fractional systems theory |
| title_full | Selected problems of fractional systems theory Tadeusz Kaczorek |
| title_fullStr | Selected problems of fractional systems theory Tadeusz Kaczorek |
| title_full_unstemmed | Selected problems of fractional systems theory Tadeusz Kaczorek |
| title_short | Selected problems of fractional systems theory |
| title_sort | selected problems of fractional systems theory |
| topic | Kontrolltheorie (DE-588)4032317-1 gnd Dynamisches System (DE-588)4013396-5 gnd Positives System (DE-588)4746300-4 gnd |
| topic_facet | Kontrolltheorie Dynamisches System Positives System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3702271&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024136257&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005848579 |
| work_keys_str_mv | AT kaczorektadeusz selectedproblemsoffractionalsystemstheory |