Polynomial control systems: analysis and design via dissipation inequalities and sum of squares
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Düsseldorf
VDI-Verl.
2006
|
| Edition: | Als Ms. gedr. |
| Series: | Fortschritt-Berichte VDI
Reihe 8, Meß-, Steuerungs- und Regelungstechnik ; 1107 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Stuttgart, Univ., Diss., 2005 |
| Physical Description: | XII, 95 S. graph. Darst. 21 cm |
| ISBN: | 318510708X |
Staff View
MARC
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| 245 | 1 | 0 | |a Polynomial control systems |b analysis and design via dissipation inequalities and sum of squares |c Christian Ebenbauer |
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| 490 | 1 | |a Fortschritt-Berichte VDI : Reihe 8, Meß-, Steuerungs- und Regelungstechnik |v 1107 | |
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| adam_text | V
Contents
Abstract vii
Deutsche Zusammenfassung viii
1 Introduction 1
1.1 Contributions 2
1.2 Outline 3
2 Background 4
2.1 Polynomial Control Systems 4
2.2 Dissipation Inequalities 6
2.3 Sum of Squares 8
2.4 Notation 11
3 Analysis 13
3.1 Preliminaries 13
3.2 Constrained Stability Analysis 14
3.2.1 Introduction 14
3.2.2 A Stability Result for Constrained Control Systems 15
3.2.3 Examples 20
3.2.4 Discussion and Summary 21
3.3 An Asymptotic Stability Result via a LaSalle type Argument 22
3.4 Minimum Phase Analysis 23
3.4.1 Introduction 23
3.4.2 Minimum Phase Property 24
3.4.3 A Dissipation Inequality for the Minimum Phase Property 26
3.4.4 Examples 31
3.4.5 Further Remarks 33
3.4.6 Discussion and Summary 35
4 Design 36
4.1 Preliminaries 36
4.2 Passive Design 37
4.2.1 Introduction 37
vi CONTENTS
4.2.2 Passivity and Feedback Passivation 38
4.2.3 A Feedback Passivation Design 39
4.2.4 Example 42
4.2.5 Discussion and Summary 45
4.3 State Feedback Design 45
4.3.1 Introduction 45
4.3.2 A State Feedback Design via Conjugate Lyapunov Functions 47
4.3.3 Example 52
4.3.4 A State Feedback Design via Krasovskii type Lyapunov Functions 53
4.3.5 Examples 56
4.3.6 Discussion and Summary 60
4.4 State Observer Design 60
4.4.1 Introduction 60
4.4.2 An Observer Design via Nonquadratic Lyapunov Functions 61
4.4.3 Examples 64
4.4.4 A High Gain Observer Design via Gain dependent Lyapunov Functions ... 65
4.4.5 Example 70
4.4.6 Discussion and Summary 72
4.5 Certainty Equivalence Output Feedback Design 73
4.5.1 Introduction 73
4.5.2 A Class of Polynomial Type Feedbacks which guarantees ISS 74
4.5.3 A Certainty Equivalence Design 79
4.5.4 Example 81
4.5.5 Discussion and Summary 82
5 Conclusions 83
5.1 Summary 83
5.2 Limitations 84
5.3 Outlook 85
Bibliography 87
|
| adam_txt |
V
Contents
Abstract vii
Deutsche Zusammenfassung viii
1 Introduction 1
1.1 Contributions 2
1.2 Outline 3
2 Background 4
2.1 Polynomial Control Systems 4
2.2 Dissipation Inequalities 6
2.3 Sum of Squares 8
2.4 Notation 11
3 Analysis 13
3.1 Preliminaries 13
3.2 Constrained Stability Analysis 14
3.2.1 Introduction 14
3.2.2 A Stability Result for Constrained Control Systems 15
3.2.3 Examples 20
3.2.4 Discussion and Summary 21
3.3 An Asymptotic Stability Result via a LaSalle type Argument 22
3.4 Minimum Phase Analysis 23
3.4.1 Introduction 23
3.4.2 Minimum Phase Property 24
3.4.3 A Dissipation Inequality for the Minimum Phase Property 26
3.4.4 Examples 31
3.4.5 Further Remarks 33
3.4.6 Discussion and Summary 35
4 Design 36
4.1 Preliminaries 36
4.2 Passive Design 37
4.2.1 Introduction 37
vi CONTENTS
4.2.2 Passivity and Feedback Passivation 38
4.2.3 A Feedback Passivation Design 39
4.2.4 Example 42
4.2.5 Discussion and Summary 45
4.3 State Feedback Design 45
4.3.1 Introduction 45
4.3.2 A State Feedback Design via Conjugate Lyapunov Functions 47
4.3.3 Example 52
4.3.4 A State Feedback Design via Krasovskii type Lyapunov Functions 53
4.3.5 Examples 56
4.3.6 Discussion and Summary 60
4.4 State Observer Design 60
4.4.1 Introduction 60
4.4.2 An Observer Design via Nonquadratic Lyapunov Functions 61
4.4.3 Examples 64
4.4.4 A High Gain Observer Design via Gain dependent Lyapunov Functions . 65
4.4.5 Example 70
4.4.6 Discussion and Summary 72
4.5 Certainty Equivalence Output Feedback Design 73
4.5.1 Introduction 73
4.5.2 A Class of Polynomial Type Feedbacks which guarantees ISS 74
4.5.3 A Certainty Equivalence Design 79
4.5.4 Example 81
4.5.5 Discussion and Summary 82
5 Conclusions 83
5.1 Summary 83
5.2 Limitations 84
5.3 Outlook 85
Bibliography 87 |
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| isbn | 318510708X |
| language | English |
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| physical | XII, 95 S. graph. Darst. 21 cm |
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| series2 | Fortschritt-Berichte VDI : Reihe 8, Meß-, Steuerungs- und Regelungstechnik |
| spelling | Ebenbauer, Christian Verfasser (DE-588)132085291 aut Polynomial control systems analysis and design via dissipation inequalities and sum of squares Christian Ebenbauer Als Ms. gedr. Düsseldorf VDI-Verl. 2006 XII, 95 S. graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Fortschritt-Berichte VDI : Reihe 8, Meß-, Steuerungs- und Regelungstechnik 1107 Zugl.: Stuttgart, Univ., Diss., 2005 Nichtlineare Regelung - Reglerentwurf - Zustandsrückführung - Beobachter <Kybernetik> - Differential-algebraisches Gleichungssystem Zustandsrückführung (DE-588)4191173-8 gnd rswk-swf Nichtlineare Regelung (DE-588)4132964-8 gnd rswk-swf Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd rswk-swf Beobachter Kybernetik (DE-588)4139504-9 gnd rswk-swf Reglerentwurf (DE-588)4177447-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Nichtlineare Regelung (DE-588)4132964-8 s Reglerentwurf (DE-588)4177447-4 s Zustandsrückführung (DE-588)4191173-8 s Beobachter Kybernetik (DE-588)4139504-9 s Differential-algebraisches Gleichungssystem (DE-588)4229517-8 s DE-604 Fortschritt-Berichte VDI Reihe 8, Meß-, Steuerungs- und Regelungstechnik ; 1107 (DE-604)BV000882482 1107 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014984316&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ebenbauer, Christian Polynomial control systems analysis and design via dissipation inequalities and sum of squares Fortschritt-Berichte VDI Nichtlineare Regelung - Reglerentwurf - Zustandsrückführung - Beobachter <Kybernetik> - Differential-algebraisches Gleichungssystem Zustandsrückführung (DE-588)4191173-8 gnd Nichtlineare Regelung (DE-588)4132964-8 gnd Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Beobachter Kybernetik (DE-588)4139504-9 gnd Reglerentwurf (DE-588)4177447-4 gnd |
| subject_GND | (DE-588)4191173-8 (DE-588)4132964-8 (DE-588)4229517-8 (DE-588)4139504-9 (DE-588)4177447-4 (DE-588)4113937-9 |
| title | Polynomial control systems analysis and design via dissipation inequalities and sum of squares |
| title_auth | Polynomial control systems analysis and design via dissipation inequalities and sum of squares |
| title_exact_search | Polynomial control systems analysis and design via dissipation inequalities and sum of squares |
| title_exact_search_txtP | Polynomial control systems analysis and design via dissipation inequalities and sum of squares |
| title_full | Polynomial control systems analysis and design via dissipation inequalities and sum of squares Christian Ebenbauer |
| title_fullStr | Polynomial control systems analysis and design via dissipation inequalities and sum of squares Christian Ebenbauer |
| title_full_unstemmed | Polynomial control systems analysis and design via dissipation inequalities and sum of squares Christian Ebenbauer |
| title_short | Polynomial control systems |
| title_sort | polynomial control systems analysis and design via dissipation inequalities and sum of squares |
| title_sub | analysis and design via dissipation inequalities and sum of squares |
| topic | Nichtlineare Regelung - Reglerentwurf - Zustandsrückführung - Beobachter <Kybernetik> - Differential-algebraisches Gleichungssystem Zustandsrückführung (DE-588)4191173-8 gnd Nichtlineare Regelung (DE-588)4132964-8 gnd Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Beobachter Kybernetik (DE-588)4139504-9 gnd Reglerentwurf (DE-588)4177447-4 gnd |
| topic_facet | Nichtlineare Regelung - Reglerentwurf - Zustandsrückführung - Beobachter <Kybernetik> - Differential-algebraisches Gleichungssystem Zustandsrückführung Nichtlineare Regelung Differential-algebraisches Gleichungssystem Beobachter Kybernetik Reglerentwurf Hochschulschrift |
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| work_keys_str_mv | AT ebenbauerchristian polynomialcontrolsystemsanalysisanddesignviadissipationinequalitiesandsumofsquares |