Fractional-order nonlinear systems: modeling, analysis and simulation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg [u.a.]
Springer [u.a.]
2011
|
| Schriftenreihe: | Nonlinear Physical Science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVI, 218 S. graph. Darst. 24 cm |
| ISBN: | 9783642181009 3642181007 9787040315349 9783642181016 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
REFERENCES 3
2 FRACTIONAL CALCULUS 7
2.1 SPECIAL FUNCTIONS 7
2.2 DEFINITIONS OF FRACTIONAL DERIVATIVES AND INTEGRALS 9
2.3 GRIINWALD-LETNIKOV FRACTIONAL INTEGRALS AND DERIVATIVES 9 2.4
RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS AND DERIVATIVES 11 2.5 CAPUTO
FRACTIONAL DERIVATIVES 12
2.6 LAPLACE TRANSFORM METHOD 12
2.6.1 BASIC FACTS ABOUT THE LAPLACE TRANSFORM 12
2.6.2 LAPLACE TRANSFORM OF FRACTIONAL INTEGRALS 14
2.6.3 LAPLACE TRANSFORM OF FRACTIONAL DERIVATIVES 14 2.7 FOURIER
TRANSFORM METHOD 15
2.7.1 BASIC FACTS ABOUTTHE FOURIER TRANSFORM 15
2.7.2 FOURIER TRANSFORM OF FRACTIONAL INTEGRALS 16
2.7.3 FOURIER TRANSFORM OF FRACTIONAL DERIVATIVES 17
2.8 SOME PROPERTIES OF FRACTIONAL DERIVATIVES AND INTEGRALS 18 2.9
NUMERICAL METHODS FOR CALCULATION OF FRACTIONAL DERIVATIVES AND
INTEGRALS 19
2.10 FRACTIONAL CALCULUS AND ELECTRICITY 29
2.10.1 ANALOGUE FRACTIONAL-ORDER CIRCUITS 35
2.10.2 EXPERIMENTAL MEASUREMENT 36
2.10.3 ADDITIONAL REMARKS 37
REFERENCES 38
3 FRACTIONAL-ORDER SYSTEMS 43
3.1 FRACTIONAL LTI SYSTEMS 43
3.2 FRACTIONAL NONLINEAR SYSTEMS 47
3.3 FRACTIONAL-ORDER CONTROLLERS 47
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/100878480X
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
3.3.1 DEFINITION OF FRACTIONAL-ORDER CONTROLLERS 47
3.3.2 PROPERTIES AND CHARACTERISTICS OF CONTROLLER 49
3.3.3 DESIGN OF CONTROLLER PARAMETERS AND IMPLEMENTATION 51 REFERENCES
52
STABILITY OF FRACTIONAL-ORDER SYSTEMS 55
4.1 PRELIMINARY CONSIDERATION 55
4.2 STABILITY OF FRACTIONAL LTI SYSTEMS 63
4.3 STABILITY OF FRACTIONAL NONLINEAR SYSTEMS 78
4.4 ROBUST STABILITY OF FRACTIONAL-ORDER LTI SYSTEMS 82
4.4.1 STABILITY CHECK WHEN THE FRACTIONAL ORDERS ARE CRISP AND
COMMENSURATE 82
4.4.2 STABILITY CHECK WHEN THE FRACTIONAL ORDERS ARE ALSO INTERVAL REAL
NUMBERS 87
4.5 STABILITY OF FRACTIONAL-ORDER NONLINEAR UNCERTAIN SYSTEMS 97
REFERENCES 98
FRACTIONAL-ORDER CHAOTIC SYSTEMS 103
5.1 INTRODUCTION TO CHAOTIC DYNAMICS 103
5.2 CONCEPT OF CHUA'S CIRCUIT .104
5.2.1 CLASSICAL CHUA'S OSCILLATOR 104
5.2.2 FRACTIONAL-ORDER CHUA'S OSCILLATOR 107
5.2.3 FRACTIONAL-ORDER CHUA-PODLUBNY'S OSCILLATOR 113 5.2.4
FRACTIONAL-ORDER CHUA-HARTLEY'S OSCILLATOR 114 5.2.5 FRACTIONAL-ORDER
MEMRISTOR-BASED CHUA'S OSCILLATOR 114 5.3 FRACTIONAL-ORDER VAN DER POL
OSCILLATOR 127
5.4 FRACTIONAL-ORDER DUFFING'S OSCILLATOR 130
5.5 FRACTIONAL-ORDER LORENZ'S SYSTEM 134
5.6 FRACTIONAL-ORDER CHEN'S SYSTEM 138
5.7 FRACTIONAL-ORDER LII'S SYSTEM 140
5.8 FRACTIONAL-ORDER LIU'S SYSTEM 142
5.9 FRACTIONAL-ORDER GENESIO-TESI'S SYSTEM 145
5.10 FRACTIONAL-ORDER ARNEODO'S SYSTEM 148
5.11 FRACTIONAL-ORDER ROESSLER'S SYSTEM 151
5.12 FRACTIONAL-ORDER NEWTON-LEIPNIK'S SYSTEM 154
5.13 FRACTIONAL-ORDER LOTKA-VOLTERRA SYSTEM 160
5.14 FRACTIONAL-ORDER FINANCIAL SYSTEM 165
5.15 FRACTIONAL-ORDER CNN 168
5.16 FRACTIONAL-ORDER VOLTA'S SYSTEM 171
REFERENCES 181
CONTROL OF FRACTIONAL-ORDER CHAOTIC SYSTEMS 185
6.1 PRELIMINARY CONSIDERATIONS 185
6.2 A SURVEY OF CONTROL STRATEGIES 187
6.3 EXAMPLES: FEED-BACK CONTROL OF CHAOTIC SYSTEMS 188
IMAGE 3
CONTENTS XIII
6.3.1 SAMPLED-DATA CONTROL OF CHUA'S OSCILLATOR 188 6.3.2 SLIDING MODE
CONTROL OF THE ECONOMICAL SYSTEM 192 REFERENCES 197
7 CONCLUSION 201
REFERENCES 203
APPENDIX A A LIST OF MATLAB FUNCTIONS 207
APPENDIX B LAPLACE AND INVERSE LAPLACE TRANSFORMS 211 GLOSSARY 215
INDEX 217 |
| any_adam_object | 1 |
| author | Petráš, Ivo |
| author_GND | (DE-588)1012618161 |
| author_facet | Petráš, Ivo |
| author_role | aut |
| author_sort | Petráš, Ivo |
| author_variant | i p ip |
| building | Verbundindex |
| bvnumber | BV040495854 |
| classification_rvk | SK 955 |
| ctrlnum | (OCoLC)740996274 (DE-599)DNB100878480X |
| dewey-full | 515.39 620 |
| dewey-hundreds | 500 - Natural sciences and mathematics 600 - Technology (Applied sciences) |
| dewey-ones | 515 - Analysis 620 - Engineering and allied operations |
| dewey-raw | 515.39 620 |
| dewey-search | 515.39 620 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics 620 - Engineering and allied operations |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-08-21T00:15:43Z |
| institution | BVB |
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| language | English |
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| physical | XVI, 218 S. graph. Darst. 24 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer [u.a.] |
| record_format | marc |
| series2 | Nonlinear Physical Science |
| spelling | Petráš, Ivo Verfasser (DE-588)1012618161 aut Fractional-order nonlinear systems modeling, analysis and simulation Ivo Petráš Berlin ; Heidelberg [u.a.] Springer [u.a.] 2011 XVI, 218 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Nonlinear Physical Science Nichtlineares System (DE-588)4042110-7 gnd rswk-swf Gebrochene Analysis (DE-588)4722475-7 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Nichtlineares System (DE-588)4042110-7 s Chaotisches System (DE-588)4316104-2 s Gebrochene Analysis (DE-588)4722475-7 s DE-604 Erscheint auch als Online-Ausgabe Petráš, Ivo Fractional-Order Nonlinear Systems X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3623734&prov=M&dok%5Fvar=1&dok%5Fext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025342744&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Petráš, Ivo Fractional-order nonlinear systems modeling, analysis and simulation Nichtlineares System (DE-588)4042110-7 gnd Gebrochene Analysis (DE-588)4722475-7 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4042110-7 (DE-588)4722475-7 (DE-588)4316104-2 |
| title | Fractional-order nonlinear systems modeling, analysis and simulation |
| title_auth | Fractional-order nonlinear systems modeling, analysis and simulation |
| title_exact_search | Fractional-order nonlinear systems modeling, analysis and simulation |
| title_full | Fractional-order nonlinear systems modeling, analysis and simulation Ivo Petráš |
| title_fullStr | Fractional-order nonlinear systems modeling, analysis and simulation Ivo Petráš |
| title_full_unstemmed | Fractional-order nonlinear systems modeling, analysis and simulation Ivo Petráš |
| title_short | Fractional-order nonlinear systems |
| title_sort | fractional order nonlinear systems modeling analysis and simulation |
| title_sub | modeling, analysis and simulation |
| topic | Nichtlineares System (DE-588)4042110-7 gnd Gebrochene Analysis (DE-588)4722475-7 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Nichtlineares System Gebrochene Analysis Chaotisches System |
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| work_keys_str_mv | AT petrasivo fractionalordernonlinearsystemsmodelinganalysisandsimulation |