Practical stability of nonlinear systems:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore u.a.
World Scientific
1990
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 207 S. |
| ISBN: | 9810203519 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV004547381 | ||
| 003 | DE-604 | ||
| 005 | 20210727 | ||
| 007 | t| | ||
| 008 | 911008s1990 xx |||| 00||| eng d | ||
| 020 | |a 9810203519 |9 981-02-0351-9 | ||
| 035 | |a (OCoLC)22346544 | ||
| 035 | |a (DE-599)BVBBV004547381 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-12 |a DE-739 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA402.3 | |
| 082 | 0 | |a 003/.74/0151535 |2 20 | |
| 082 | 0 | |a 003.750151535 |2 20 | |
| 084 | |a SK 520 |0 (DE-625)143244: |2 rvk | ||
| 084 | |a SK 880 |0 (DE-625)143266: |2 rvk | ||
| 084 | |a MAT 345f |2 stub | ||
| 100 | 1 | |a Lakshmikantham, Vangipuram |d 1926-2012 |e Verfasser |0 (DE-588)104268050 |4 aut | |
| 245 | 1 | 0 | |a Practical stability of nonlinear systems |c V. Lashmikantham ; S. Leela ; A. A. Martynyuk |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1990 | |
| 300 | |a VIII, 207 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Lyapunov functions | |
| 650 | 4 | |a Stability | |
| 650 | 0 | 7 | |a Nichtlineares System |0 (DE-588)4042110-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stabilität |0 (DE-588)4056693-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare gewöhnliche Differentialgleichung |0 (DE-588)4478411-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineares System |0 (DE-588)4042110-7 |D s |
| 689 | 0 | 1 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Stabilität |0 (DE-588)4056693-6 |D s |
| 689 | 1 | 1 | |a Nichtlineare gewöhnliche Differentialgleichung |0 (DE-588)4478411-9 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Leela, Srinivasa |d 1936- |e Verfasser |0 (DE-588)123072417 |4 aut | |
| 700 | 1 | |a Martynjuk, Anatolij A. |d 1941- |e Verfasser |0 (DE-588)1020347279 |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002798103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-002798103 | |
Record in the Search Index
| _version_ | 1826831278383562752 |
|---|---|
| adam_text |
Contents
Preface v
Chapter 1. What is Practical Stability? 1
1.0. Introduction 1
1.1. Definitions of Lyapunov stability 2
1.2. Definitions of practical stability g
1.3. Stability criteria 12
1.4. Delay differential equations 22
1.5. Integro differential equations 26
1.6. Difference equations 30
1.7. Impulsive differential equations 40
1.8. Notes 51
Chapter 2. Method of Lyapunov Functions. 53
2.0. Introduction 53
2.1. Basic comparison theorems 54
2.2. Stability criteria 59
2.3. Perturbing Lyapunov functions 70
2.4. Several Lyapunov functions 74
vii
viii Contents
2.5. Large scale dynamic systems 77
2.6. General definitions of practical stability 80
2.7. Stability criteria in terms of two measures 84
2.8. Global results in terms of sets 91
2.9. Stability criteria in terms of sets 97
2.10. Notes 101
Chapter 3. Perturbed Systems. 103
3.0. Introduction 103
3.1. Stability of perturbed systems 104
3.2. Stability of perturbed systems (continued) 108
3.3. A technique in perturbation theory 111
3.4. Difference equations 119
3.5. Delay differential equations 122
3.6. Integro differential equations of Volterra type 127
3.7. Impulsive differential systems 131
3.8. Impulsive integro differential equations 138
3.9. Reaction diffusion equations 145
3.10. Notes 155
Chapter 4. Control Systems. 157
4.0. Introduction 157
4.1. Control systems 158
4.2. Controllable systems 164
4.3. Decentralized control systems 169
4.4. Optimal controllability * 173
4.5. Set valued differential inequalities 177
4.6. Practical stability criteria 182
4.7. Notes 186
Appendix 189
A.I. Differential inequalities 189
A.2. Integro differential equations 195
A.3. Impulsive differential inequalities 196
References 199 |
| any_adam_object | 1 |
| author | Lakshmikantham, Vangipuram 1926-2012 Leela, Srinivasa 1936- Martynjuk, Anatolij A. 1941- |
| author_GND | (DE-588)104268050 (DE-588)123072417 (DE-588)1020347279 |
| author_facet | Lakshmikantham, Vangipuram 1926-2012 Leela, Srinivasa 1936- Martynjuk, Anatolij A. 1941- |
| author_role | aut aut aut |
| author_sort | Lakshmikantham, Vangipuram 1926-2012 |
| author_variant | v l vl s l sl a a m aa aam |
| building | Verbundindex |
| bvnumber | BV004547381 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.3 |
| callnumber-search | QA402.3 |
| callnumber-sort | QA 3402.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 520 SK 880 |
| classification_tum | MAT 345f |
| ctrlnum | (OCoLC)22346544 (DE-599)BVBBV004547381 |
| dewey-full | 003/.74/0151535 003.750151535 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003/.74/0151535 003.750151535 |
| dewey-search | 003/.74/0151535 003.750151535 |
| dewey-sort | 13 274 6151535 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV004547381</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210727</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">911008s1990 xx |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9810203519</subfield><subfield code="9">981-02-0351-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)22346544</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV004547381</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA402.3</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">003/.74/0151535</subfield><subfield code="2">20</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">003.750151535</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 520</subfield><subfield code="0">(DE-625)143244:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 880</subfield><subfield code="0">(DE-625)143266:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 345f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lakshmikantham, Vangipuram</subfield><subfield code="d">1926-2012</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)104268050</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Practical stability of nonlinear systems</subfield><subfield code="c">V. Lashmikantham ; S. Leela ; A. A. Martynyuk</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore u.a.</subfield><subfield code="b">World Scientific</subfield><subfield code="c">1990</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 207 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Control theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lyapunov functions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stability</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineares System</subfield><subfield code="0">(DE-588)4042110-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stabilität</subfield><subfield code="0">(DE-588)4056693-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4478411-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ljapunov-Stabilitätstheorie</subfield><subfield code="0">(DE-588)4167992-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineares System</subfield><subfield code="0">(DE-588)4042110-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Ljapunov-Stabilitätstheorie</subfield><subfield code="0">(DE-588)4167992-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Stabilität</subfield><subfield code="0">(DE-588)4056693-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Nichtlineare gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4478411-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Leela, Srinivasa</subfield><subfield code="d">1936-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)123072417</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Martynjuk, Anatolij A.</subfield><subfield code="d">1941-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1020347279</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002798103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-002798103</subfield></datafield></record></collection> |
| id | DE-604.BV004547381 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-17T09:01:10Z |
| institution | BVB |
| isbn | 9810203519 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002798103 |
| oclc_num | 22346544 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-12 DE-739 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-12 DE-739 DE-11 DE-188 |
| physical | VIII, 207 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Lakshmikantham, Vangipuram 1926-2012 Verfasser (DE-588)104268050 aut Practical stability of nonlinear systems V. Lashmikantham ; S. Leela ; A. A. Martynyuk Singapore u.a. World Scientific 1990 VIII, 207 S. txt rdacontent n rdamedia nc rdacarrier Control theory Differential equations Lyapunov functions Stability Nichtlineares System (DE-588)4042110-7 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Nichtlineares System (DE-588)4042110-7 s Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s DE-604 Stabilität (DE-588)4056693-6 s Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 s Leela, Srinivasa 1936- Verfasser (DE-588)123072417 aut Martynjuk, Anatolij A. 1941- Verfasser (DE-588)1020347279 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002798103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lakshmikantham, Vangipuram 1926-2012 Leela, Srinivasa 1936- Martynjuk, Anatolij A. 1941- Practical stability of nonlinear systems Control theory Differential equations Lyapunov functions Stability Nichtlineares System (DE-588)4042110-7 gnd Stabilität (DE-588)4056693-6 gnd Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| subject_GND | (DE-588)4042110-7 (DE-588)4056693-6 (DE-588)4478411-9 (DE-588)4167992-1 |
| title | Practical stability of nonlinear systems |
| title_auth | Practical stability of nonlinear systems |
| title_exact_search | Practical stability of nonlinear systems |
| title_full | Practical stability of nonlinear systems V. Lashmikantham ; S. Leela ; A. A. Martynyuk |
| title_fullStr | Practical stability of nonlinear systems V. Lashmikantham ; S. Leela ; A. A. Martynyuk |
| title_full_unstemmed | Practical stability of nonlinear systems V. Lashmikantham ; S. Leela ; A. A. Martynyuk |
| title_short | Practical stability of nonlinear systems |
| title_sort | practical stability of nonlinear systems |
| topic | Control theory Differential equations Lyapunov functions Stability Nichtlineares System (DE-588)4042110-7 gnd Stabilität (DE-588)4056693-6 gnd Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| topic_facet | Control theory Differential equations Lyapunov functions Stability Nichtlineares System Stabilität Nichtlineare gewöhnliche Differentialgleichung Ljapunov-Stabilitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002798103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lakshmikanthamvangipuram practicalstabilityofnonlinearsystems AT leelasrinivasa practicalstabilityofnonlinearsystems AT martynjukanatolija practicalstabilityofnonlinearsystems |