Stability of dynamical systems: continuous, discontinuous, and discrete systems
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2007
|
| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | Systems & control: Foundations & applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 501 S. graph. Darst. |
| ISBN: | 9780817644864 |
Internformat
MARC
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| 008 | 070315s2007 d||| |||| 00||| eng d | ||
| 020 | |a 9780817644864 |9 978-0-8176-4486-4 | ||
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| 100 | 1 | |a Michel, Anthony N. |d 1935- |e Verfasser |0 (DE-588)11087076X |4 aut | |
| 245 | 1 | 0 | |a Stability of dynamical systems |b continuous, discontinuous, and discrete systems |c Anthony N. Michel ; Ling Hou ; Derong Liu |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2007 | |
| 300 | |a XII, 501 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Systems & control: Foundations & applications | |
| 650 | 7 | |a Liapounov, Stabilité de |2 ram | |
| 650 | 7 | |a Stabilité |2 ram | |
| 650 | 7 | |a Systèmes dynamiques |2 ram | |
| 650 | 7 | |a Équations différentielles |2 ram | |
| 650 | 0 | 7 | |a Stabilität |0 (DE-588)4056693-6 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Stabilität |0 (DE-588)4056693-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Hou, Ling |e Verfasser |0 (DE-588)133728080 |4 aut | |
| 700 | 1 | |a Liu, Derong |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015522404&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015522404 | ||
Datensatz im Suchindex
| _version_ | 1804136334789443584 |
|---|---|
| adam_text | Contents
Preface
xi
1
Introduction
1
1.1
Dynamical Systems
.......................... 1
1.2
A Brief Perspective on the Development of Stability Theory
.... 4
1.3
Scope and Contents of the Book
................... 6
Bibliography
................................ 12
2
Dynamical Systems
17
2.1
Notation
................................ 18
2.2
Dynamical Systems
.......................... 19
2.3
Ordinary Differential Equations
................... 20
2.4
Ordinary Differential Inequalities
................... 26
2.5
Difference Equations and Inequalities
. . .·............. 26
2.6
Differential Equations and Inclusions Defined on Banach Spaces
. . 28
2.7
Functional Differential Equations
................... 31
2.8
Volterra Integrodifferential Equations
................ 34
2.9
Semigroups
.............................. 38
2.10
Partial Differential Equations
..................... 46
2.11
Composite Dynamical Systems
.................... 51
2.12
Discontinuous Dynamical Systems
.................. 52
2.13
Notes and References
......................... 59
2.14
Problems
............................... 61
Bibliography
................................ 67
3
Fundamental Theory: The Principal Stability and Boundedness
Results on Metric Spaces
71
3.1
Some Qualitative Characterizations of Dynamical Systems
..... 73
3.2
The Principal Lyapunov and
Lagrange
Stability Results for
Discontinuous Dynamical Systems
.................. 82
vii
¡
Contents
3.3
The Principal Lyapunov and
Lagrange
Stability Results for
Continuous Dynamical Systems
................... 92
3.4
The Principal Lyapunov and
Lagrange
Stability Results for
Discrete-Time Dynamical Systems
.................. 103
3.5
Converse Theorems for Discontinuous Dynamical Systems
..... 112
3.6
Converse Theorems for Continuous Dynamical Systems
...... 125
3.7
Converse Theorems for Discrete-Time Dynamical Systems
..... 133
3.8
Appendix: Some Background Material on Differential Equations
. . 137
3.9
Notes and References
......................... 141
3.10
Problems
............................... 142
Bibliography
................................ 147
Fundamental Theory: Specialized Stability and Boundedness
Results on Metric Spaces
149
4.1
Autonomous Dynamical Systems
................... 149
4.2
Invariance
Theory
........................... 153
4.3
Comparison Theory
.......................... 158
4.4
Uniqueness of Motions
........................ 165
4.5
Notes and References
......................... 167
4.6
Problems
............................... 167
Bibliography
................................ 172
Applications to a Class of Discrete-Event Systems
173
5.1
A Class of Discrete-Event Systems
.................. 173
5.2
Stability Analysis of Discrete-Event Systems
............ 175
5.3
Analysis of a Manufacturing System
................. 176
5.4
Load Balancing in a Computer Network
............... 179
5.5
Notes and References
......................... 181
5.6
Problems
............................... 181
Bibliography
................................ 182
Finite-Dimensional Dynamical Systems
185
6.1
Preliminaries
............................. 185
6.2
The Principal Stability and Boundedness Results for Ordinary
Differential Equations
......................... 199
6.3
The Principal Stability and Boundedness Results for Ordinary
Difference Equations
......................... 211
6.4
The Principal Stability and Boundedness Results for Discontinuous
Dynamical Systems
.......................... 219
6.5
Converse Theorems for Ordinary Differential Equations
....... 232
6.6
Converse Theorems for Ordinary Difference Equations
....... 241
Contents ix
6.7
Converse
Theorems
for Finite-Dimensional DDS
.......... 243
6.8
Appendix: Some Background Material on Differential Equations
. . 245
6.9
Notes and References
......................... 249
6.10
Problems
............................... 250
Bibliography
................................ 253
7
Finite-Dimensional Dynamical Systems: Specialized Results
255
7.1
Autonomous and Periodic Systems
.................. 256
7.2
Invariance
Theory
........................... 258
7.3
Domain of Attraction
......................... 263
7.4
Linear Continuous-Time Systems
.................. 266
7.5
Linear Discrete-Time Systems
.................... 285
7.6
Perturbed Linear Systems
....................... 295
7.7
Comparison Theory
.......................... 316
7.8
Appendix: Background Material on Differential Equations and
Difference Equations
......................... 320
7.9
Notes and References
......................... 328
7.10
Problems
............................... 329
Bibliography
................................ 335
8
Applications to Finite-Dimensional Dynamical Systems
337
8.1
Absolute Stability of Regulator Systems
............... 338
8.2
Hopfield Neural Networks
...................... 344
8.3
Digital Control Systems
........................ 353
8.4
Pulse-Width-Modulated Feedback Control Systems
......... 364
8.5
Digital Filters
............................. 376
8.6
Notes and References
......................... 387
Bibliography
................................ 389
9
Infinite-Dimensional Dynamical Systems
395
9.1
Preliminaries
............................. 396
9.2
The Principal Lyapunov Stability and Boundedness Results for
Differential Equations in Banach Spaces
............... 398
9.3
Converse Theorems for Differential Equations in Banach Spaces
. . 408
9.4
Invariance
Theory for Differential Equations in Banach Spaces
. . . 409
9.5
Comparison Theory for Differential Equations in Banach Spaces
. . 413
9.6
Composite Systems
.......................... 415
9.7
Analysis of a Point Kinetics Model of a Multicore Nuclear Reactor
. 420
9.8
Results for Retarded Functional Differential Equations
....... 423
9.9
Applications to a Class of
Artificia!
Neural Networks with Time
Delays
................................. 438
χ
Contents
9.10
Discontinuous Dynamical Systems Determined by Differential
Equations in Banach Spaces
..................... 449
9.11
Discontinuous Dynamical Systems Determined by Semigroups
. . . 463
9.12
Notes and References
......................... 479
9.13
Problems
............................... 480
Bibliography
................................ 486
Index
489
|
| adam_txt |
Contents
Preface
xi
1
Introduction
1
1.1
Dynamical Systems
. 1
1.2
A Brief Perspective on the Development of Stability Theory
. 4
1.3
Scope and Contents of the Book
. 6
Bibliography
. 12
2
Dynamical Systems
17
2.1
Notation
. 18
2.2
Dynamical Systems
. 19
2.3
Ordinary Differential Equations
. 20
2.4
Ordinary Differential Inequalities
. 26
2.5
Difference Equations and Inequalities
. . .·. 26
2.6
Differential Equations and Inclusions Defined on Banach Spaces
. . 28
2.7
Functional Differential Equations
. 31
2.8
Volterra Integrodifferential Equations
. 34
2.9
Semigroups
. 38
2.10
Partial Differential Equations
. 46
2.11
Composite Dynamical Systems
. 51
2.12
Discontinuous Dynamical Systems
. 52
2.13
Notes and References
. 59
2.14
Problems
. 61
Bibliography
. 67
3
Fundamental Theory: The Principal Stability and Boundedness
Results on Metric Spaces
71
3.1
Some Qualitative Characterizations of Dynamical Systems
. 73
3.2
The Principal Lyapunov and
Lagrange
Stability Results for
Discontinuous Dynamical Systems
. 82
vii
¡
Contents
3.3
The Principal Lyapunov and
Lagrange
Stability Results for
Continuous Dynamical Systems
. 92
3.4
The Principal Lyapunov and
Lagrange
Stability Results for
Discrete-Time Dynamical Systems
. 103
3.5
Converse Theorems for Discontinuous Dynamical Systems
. 112
3.6
Converse Theorems for Continuous Dynamical Systems
. 125
3.7
Converse Theorems for Discrete-Time Dynamical Systems
. 133
3.8
Appendix: Some Background Material on Differential Equations
. . 137
3.9
Notes and References
. 141
3.10
Problems
. 142
Bibliography
. 147
Fundamental Theory: Specialized Stability and Boundedness
Results on Metric Spaces
149
4.1
Autonomous Dynamical Systems
. 149
4.2
Invariance
Theory
. 153
4.3
Comparison Theory
. 158
4.4
Uniqueness of Motions
. 165
4.5
Notes and References
. 167
4.6
Problems
. 167
Bibliography
. 172
Applications to a Class of Discrete-Event Systems
173
5.1
A Class of Discrete-Event Systems
. 173
5.2
Stability Analysis of Discrete-Event Systems
. 175
5.3
Analysis of a Manufacturing System
. 176
5.4
Load Balancing in a Computer Network
. 179
5.5
Notes and References
. 181
5.6
Problems
. 181
Bibliography
. 182
Finite-Dimensional Dynamical Systems
185
6.1
Preliminaries
. 185
6.2
The Principal Stability and Boundedness Results for Ordinary
Differential Equations
. 199
6.3
The Principal Stability and Boundedness Results for Ordinary
Difference Equations
. 211
6.4
The Principal Stability and Boundedness Results for Discontinuous
Dynamical Systems
. 219
6.5
Converse Theorems for Ordinary Differential Equations
. 232
6.6
Converse Theorems for Ordinary Difference Equations
. 241
Contents ix
6.7
Converse
Theorems
for Finite-Dimensional DDS
. 243
6.8
Appendix: Some Background Material on Differential Equations
. . 245
6.9
Notes and References
. 249
6.10
Problems
. 250
Bibliography
. 253
7
Finite-Dimensional Dynamical Systems: Specialized Results
255
7.1
Autonomous and Periodic Systems
. 256
7.2
Invariance
Theory
. 258
7.3
Domain of Attraction
. 263
7.4
Linear Continuous-Time Systems
. 266
7.5
Linear Discrete-Time Systems
. 285
7.6
Perturbed Linear Systems
. 295
7.7
Comparison Theory
. 316
7.8
Appendix: Background Material on Differential Equations and
Difference Equations
. 320
7.9
Notes and References
. 328
7.10
Problems
. 329
Bibliography
. 335
8
Applications to Finite-Dimensional Dynamical Systems
337
8.1
Absolute Stability of Regulator Systems
. 338
8.2
Hopfield Neural Networks
. 344
8.3
Digital Control Systems
. 353
8.4
Pulse-Width-Modulated Feedback Control Systems
. 364
8.5
Digital Filters
. 376
8.6
Notes and References
. 387
Bibliography
. 389
9
Infinite-Dimensional Dynamical Systems
395
9.1
Preliminaries
. 396
9.2
The Principal Lyapunov Stability and Boundedness Results for
Differential Equations in Banach Spaces
. 398
9.3
Converse Theorems for Differential Equations in Banach Spaces
. . 408
9.4
Invariance
Theory for Differential Equations in Banach Spaces
. . . 409
9.5
Comparison Theory for Differential Equations in Banach Spaces
. . 413
9.6
Composite Systems
. 415
9.7
Analysis of a Point Kinetics Model of a Multicore Nuclear Reactor
. 420
9.8
Results for Retarded Functional Differential Equations
. 423
9.9
Applications to a Class of
Artificia!
Neural Networks with Time
Delays
. 438
χ
Contents
9.10
Discontinuous Dynamical Systems Determined by Differential
Equations in Banach Spaces
. 449
9.11
Discontinuous Dynamical Systems Determined by Semigroups
. . . 463
9.12
Notes and References
. 479
9.13
Problems
. 480
Bibliography
. 486
Index
489 |
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| id | DE-604.BV022312904 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:59:02Z |
| indexdate | 2024-07-09T20:54:45Z |
| institution | BVB |
| isbn | 9780817644864 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015522404 |
| oclc_num | 494502310 |
| open_access_boolean | |
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| owner_facet | DE-824 DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM |
| physical | XII, 501 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Systems & control: Foundations & applications |
| spelling | Michel, Anthony N. 1935- Verfasser (DE-588)11087076X aut Stability of dynamical systems continuous, discontinuous, and discrete systems Anthony N. Michel ; Ling Hou ; Derong Liu 1. Aufl. Boston [u.a.] Birkhäuser 2007 XII, 501 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Systems & control: Foundations & applications Liapounov, Stabilité de ram Stabilité ram Systèmes dynamiques ram Équations différentielles ram Stabilität (DE-588)4056693-6 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Stabilität (DE-588)4056693-6 s DE-604 Hou, Ling Verfasser (DE-588)133728080 aut Liu, Derong Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015522404&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Michel, Anthony N. 1935- Hou, Ling Liu, Derong Stability of dynamical systems continuous, discontinuous, and discrete systems Liapounov, Stabilité de ram Stabilité ram Systèmes dynamiques ram Équations différentielles ram Stabilität (DE-588)4056693-6 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4056693-6 (DE-588)4013396-5 |
| title | Stability of dynamical systems continuous, discontinuous, and discrete systems |
| title_auth | Stability of dynamical systems continuous, discontinuous, and discrete systems |
| title_exact_search | Stability of dynamical systems continuous, discontinuous, and discrete systems |
| title_exact_search_txtP | Stability of dynamical systems continuous, discontinuous, and discrete systems |
| title_full | Stability of dynamical systems continuous, discontinuous, and discrete systems Anthony N. Michel ; Ling Hou ; Derong Liu |
| title_fullStr | Stability of dynamical systems continuous, discontinuous, and discrete systems Anthony N. Michel ; Ling Hou ; Derong Liu |
| title_full_unstemmed | Stability of dynamical systems continuous, discontinuous, and discrete systems Anthony N. Michel ; Ling Hou ; Derong Liu |
| title_short | Stability of dynamical systems |
| title_sort | stability of dynamical systems continuous discontinuous and discrete systems |
| title_sub | continuous, discontinuous, and discrete systems |
| topic | Liapounov, Stabilité de ram Stabilité ram Systèmes dynamiques ram Équations différentielles ram Stabilität (DE-588)4056693-6 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Liapounov, Stabilité de Stabilité Systèmes dynamiques Équations différentielles Stabilität Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015522404&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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