Time-delay systems: Lyapunov functionals and matrices
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Birkhäuser
2013
|
| Series: | Control engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 311 S. |
| ISBN: | 9780817683665 |
Staff View
MARC
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| 100 | 1 | |a Charitonov, Vladimir L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Time-delay systems |b Lyapunov functionals and matrices |c Vladimir L. Kharitonov |
| 264 | 1 | |a New York u.a. |b Birkhäuser |c 2013 | |
| 300 | |a XVI, 311 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Control engineering | |
| 650 | 4 | |a Feedback control systems | |
| 650 | 4 | |a Matrices | |
| 650 | 4 | |a Time delay systems | |
| 650 | 0 | 7 | |a Zeitverzögertes System |0 (DE-588)4780926-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ljapunov-Funktion |0 (DE-588)4274502-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zeitverzögertes System |0 (DE-588)4780926-7 |D s |
| 689 | 0 | 1 | |a Kontrolltheorie |0 (DE-588)4032317-1 |D s |
| 689 | 0 | 2 | |a Ljapunov-Funktion |0 (DE-588)4274502-0 |D s |
| 689 | 0 | |5 DE-604 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-026130420 | ||
Record in the Search Index
| _version_ | 1804150558852907008 |
|---|---|
| adam_text | Contents
Part X Retarded Type Systems
1 Generał
Theory
............................................................... 3
1.1
Preliminaries
............................................,,,,...,....... 3
1.1.1
Initial Value Problem
........................................ 3
1.1.2
Solutions
...................,,................................ 4
]. 1.3
State Concept
................................................ 5
1.2
Existence and Uniqueness Issues
.............................,....... 5
1.3
Continuity Properties
................................................. 11
1.4
Stability Concepts
..................................................... 13
1.5
Lyapunov-Krasovskii Approach
..................................... 14
1.6
Notes and References
.................................................. 26
2
Single Delay Case
............................................................ 27
2.1
Preliminaries
........................................................... 28
2.1.1
Fundamental Matrix
......................................... 28
2.1.2
Cauchy Formula
............................................. 29
2.2
Exponential Stability
.................................................. 30
2.3
Problem Formulation
................................................. 31
2.4
Delay-Free Case
....................................................... 32
2.5
Computation of
νο(φ)
................................................. 33
2.6
Lyapunov Matrices: Basic Properties
............................ — 37
2.7
Lyapunov Matrices; Limit Case
...................................... 43
2.8
Lyapunov Matrices: New Definition
................................. 44
2.9
Lyapunov Matrices: Existence and Uniqueness Issues
.........----- 47
?.. 10
Lyapunov Matrices: Computational Issue
........................... 56
2.
і
1
Complete Type Functionals
..........................................
Jo
?.. 1 ?,
Applications
............................................................ 62
2.12.1
Quadratic Performance Index
.....,......................... 62
2.12.2
Exponential Estimates
....................................... 63
xii Contents
2.12.3
Critical Values of Delay
..................................... 68
2.12.4
Robustness Bounds
.......................................... 69
2.13
Notes and References
................................................. 73
3
Multiple Delay Case
......................................................... 75
3.1
Preliminaries
.......................................................... 75
3.2
Quadratic Functional
................................................. 77
3.3
Lyapunov Matrices
.................................................... 93
3.3.1
Exponentially Stable Case
.................................. 93
3.3.2
General Case
................................................. 94
3.4
Computational Schemes
.............................................. 106
3.4.1
Semianalytic Method
........................................ 106
3.4.2
Scalar Equation
..............................................
Ill
3.4.3
Numerical Scheme
........................................... 113
3.4.4
Error Estimation
.............................................. 116
3.5
Exponential Estimates
................................................ 122
3.6
Robustness Bounds
................................................... 124
3.6.1
Robust Stability Conditions: General Case
................. 124
3.6.2
Robust Stability Conditions: Scalar Case
................... 125
3.7
Applications
............................................................ 127
3.7.1
Critical Values
............................................... 127
3.7.2
The H2 Norm of a Transfer Matrix
......................... 130
3.8
Notes and References
.................................................. 131
4
Systems with Distributed Delay
............................................ 133
4.1
System Description
................................................... 133
4.2
Quadratic Functionals
................................................. 133
4.3
Lyapunov Matrices: Existence Issue
................................. 141
4.4
Lyapunov Matrices: Uniqueness Issue
............................... 145
4.5
Lyapunov Matrices: Computational Issue
........................... 151
4.5.1
A Particular Case
............................................. 151
4.5.2
A Special Case
............................................... 159
4.5.3
Numerical Scheme
........................................... 162
4.6
Compiete
Type Functionals
.......................................... 164
4.7
Exponential Estimates
................................................ 168
Pari
II Neutral Type System
5
General Theory
............................................................... 173
5.1
System Description
...................,............................... 173
5.2
Existence Issue
........................................................ 175
5.3
Continuity of Solutions
............................................... 181
5.4
Stability Concepts
..................................................... 184
5.5
Lyapunov-Krasovsldi Approach
..................................... 185
5.6
Notes and References
.................................................. 200
Contents
xín
6
Linear Systems
............................................................... 201
6.1
Preliminaries
........................................................... 201
6.1.1
Fundamental Matrix
......................................... 202
6.1.2
Cauchy Formula
............................................. 203
6.2
Lyapunov Matrices: Stable Case
..................................... 204
6.3
Functional v0
(ψ)
..................................................···■
211
6.4
Lyapunov Matrices: General Case
................................... 212
6.5
Existence and Uniqueness of Lyapunov Matrices
................... 220
6.6
Computational Issue
.................................................. 236
6.7
Spectral Properties
.................................................... 237
6.8
A New Form for Lyapunov Functionals
............................. 239
6.9
Complete Type Functionals
.......................................... 243
6.10
Quadratic Bounds
..................................................... 244
6.11
Applications
............................................................ 249
6.11.1
Exponential Estimates
....................................... 249
6.11.2
Quadratic Performance Index
............................... 252
6.11.3
Robustness Bounds
.......................................... 253
6.12
Notes and References
................................................. 254
7
Distributed Delay Case
...................................................... 255
7.1
Preliminaries
....................................................__... 255
7.1.1
Fundamental Matrix
......................................... 256
7.1.2
Cauchy Formula
.............................................. 256
7.2
Lyapunov Functionals
................................................. 257
7.3
Lyapunov Matrices
.................................................... 258
7.4
Lyapunov Matrices: New Definition
.................................. 260
7.5
Existence Issue
........................................................ 273
7.6
Computation Issue
..................................................... 281
7.6.1
A Particular Case
............................................. 281
7.6.2
A Special Case
............................................... 288
7.7
A New Form of Lyapunov Functionals
............................... 291
7.8
Complete Type Functionals
........................................... 296
7.9
Quadratic Bounds
..................................................... 298
7.10
The
П2
Norm of a Transfer Matrix
................................... 303
References
........................................................................ 305
Index
...................................................,...,.,..................... 309
|
| any_adam_object | 1 |
| author | Charitonov, Vladimir L. |
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| author_sort | Charitonov, Vladimir L. |
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| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
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| dewey-search | 629.8 629.83 |
| dewey-sort | 3629.8 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Book |
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| id | DE-604.BV041155028 |
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| indexdate | 2024-07-10T00:40:50Z |
| institution | BVB |
| isbn | 9780817683665 |
| language | English |
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| physical | XVI, 311 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Control engineering |
| spelling | Charitonov, Vladimir L. Verfasser aut Time-delay systems Lyapunov functionals and matrices Vladimir L. Kharitonov New York u.a. Birkhäuser 2013 XVI, 311 S. txt rdacontent n rdamedia nc rdacarrier Control engineering Feedback control systems Matrices Time delay systems Zeitverzögertes System (DE-588)4780926-7 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Ljapunov-Funktion (DE-588)4274502-0 gnd rswk-swf Zeitverzögertes System (DE-588)4780926-7 s Kontrolltheorie (DE-588)4032317-1 s Ljapunov-Funktion (DE-588)4274502-0 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026130420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Charitonov, Vladimir L. Time-delay systems Lyapunov functionals and matrices Feedback control systems Matrices Time delay systems Zeitverzögertes System (DE-588)4780926-7 gnd Kontrolltheorie (DE-588)4032317-1 gnd Ljapunov-Funktion (DE-588)4274502-0 gnd |
| subject_GND | (DE-588)4780926-7 (DE-588)4032317-1 (DE-588)4274502-0 |
| title | Time-delay systems Lyapunov functionals and matrices |
| title_auth | Time-delay systems Lyapunov functionals and matrices |
| title_exact_search | Time-delay systems Lyapunov functionals and matrices |
| title_full | Time-delay systems Lyapunov functionals and matrices Vladimir L. Kharitonov |
| title_fullStr | Time-delay systems Lyapunov functionals and matrices Vladimir L. Kharitonov |
| title_full_unstemmed | Time-delay systems Lyapunov functionals and matrices Vladimir L. Kharitonov |
| title_short | Time-delay systems |
| title_sort | time delay systems lyapunov functionals and matrices |
| title_sub | Lyapunov functionals and matrices |
| topic | Feedback control systems Matrices Time delay systems Zeitverzögertes System (DE-588)4780926-7 gnd Kontrolltheorie (DE-588)4032317-1 gnd Ljapunov-Funktion (DE-588)4274502-0 gnd |
| topic_facet | Feedback control systems Matrices Time delay systems Zeitverzögertes System Kontrolltheorie Ljapunov-Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026130420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT charitonovvladimirl timedelaysystemslyapunovfunctionalsandmatrices |