Robust stability and convexity: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London u.a.
Springer
1995
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| Series: | Lecture notes in control and information sciences
201 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 176 S. graph. Darst. |
| ISBN: | 3540199195 0387199195 |
Staff View
MARC
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| 100 | 1 | |a Kogan, Jacob |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Robust stability and convexity |b an introduction |c Jacob Kogan |
| 264 | 1 | |a London u.a. |b Springer |c 1995 | |
| 300 | |a XI, 176 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in control and information sciences |v 201 | |
| 650 | 7 | |a Algèbres convexes |2 ram | |
| 650 | 7 | |a Commande, théorie de la |2 ram | |
| 650 | 7 | |a Regeltechniek |2 gtt | |
| 650 | 7 | |a Stabilité |2 ram | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Convex domains | |
| 650 | 4 | |a Stability | |
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Record in the Search Index
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Contents
1 Introduction and Motivation 1
1.1 Illustration 1
1.2 Stability and Convexity 2
2 Stability of Box Polynomial Families 7
2.1 Kharitonov's Theorem 7
2.2 Other root location regions: fl stability 10
2.3 Principal Vertices and Stability 11
2.4 Principal Directions and Principal Vertices 13
2.5 Principal Vertices and Testing Family 18
2.6 Examples: Schur, Hurwitz, and Sector Stability 20
2.7 Hurwitz Stability of Weighted Diamonds 23
2.8 Extreme Point Results 29
2.8.1 Sector Stability of Box Polynomials 30
2.8.2 Hurwitz Stability of Diamond Polynomials 31
3 Stability Radii and Convex Analysis 37
3.1 Stability Radii and Degree Dropping 38
3.2 Constrained Optimization Problem 44
3.3 Complex Stability Radius 44
3.4 Stability Radius 46
3.4.1 Convex Duality Results 46
3.4.2 Dual Optimization Problem 48
3.4.3 Special Cases: lr Norms 48
3.5 Examples: Stability Radii for Schur and Hurwitz Polynomials 49
X
3.6 Real Stability Radius: Examples 52
3.7 Link to Structured Matrix Perturbations 55
3.8 Matrix Perturbations 56
3.9 Multiple Matrix Perturbations and \i 60
4 Multiaffine Polynomial Families 63
4.1 Orientation Preserving Multiaffine Transformation 65
4.1.1 Image of a Two Dimensional Box 66
4.1.2 Image of a Box Under Orientation Preserving Transformation . 68
4.2 Image of a Box Under Multiaffine Transformation 73
4.2.1 Proof of Main Result 75
4.3 Robust Stability of Multiaffine Polynomial Families 75
4.4 Cascade of Uncertain Blocks 76
4.4.1 Principal Edges and Principal Segments 81
4.5 Interval Plants with Interval Controllers 84
4.5.1 Eight Faces Theorem 87
4.5.2 Frequency Domain Criterion 90
4.6 Numerical Example 93
5 Multidimensional Systems and Systems with Commensurate Delays 99
5.1 Stability of linear systems and zeros of characteristic polynomials . . . 100
5.2 Stability of a Bivariate Polynomial 102
5.3 Stability Radius 103
5.4 Reduction to the Polynomial Problem 104
5.5 Evaluation of Stability Radius 107
5.6 Example: Hurwitz Stability of Interval Bivariate Polynomials 109
5.7 Quasipolynomials with Commensurate Delays and Zero Exclusion Cri¬
terion 110
5.8 Diamond Quasipolynomials: Eight Edges Theorem 113
6 Uncertain Time Delay Systems 117
6.1 Time Delay Systems and Zero Exclusion Criterion 118
6.1.1 Proof of Zero Exclusion Criterion 119
6.2 Real Interval Quasipolynomials 121
6.3 Kharitonov Rectangles and Robust Stability Conditions 121
6.4 Image of a Box Under Nonlinear Mapping 124
6.5 Principal Segments 127
6.6 Numerical Example 129
Al
6.7 Eight Edges Theorem 131
7 Convexity of Frequency Response Arcs Associated with Hurwitz
Quasipolynomials 137
7.1 Convexity for Entire Functions 138
7.2 Angular Derivative Formalism 144
7.3 Computation of Angular Derivatives 146
7.4 Inner Frequency Response Set 148
8 Epilogue 153
8.1 Lyapunov Criterion 154
8.2 Simultaneous Stabilization 155
Bibliography 157
List of Special Symbols 170
Author Index 172
Subject Index 175 |
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| discipline | Informatik Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik |
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| illustrated | Illustrated |
| indexdate | 2024-07-20T05:21:28Z |
| institution | BVB |
| isbn | 3540199195 0387199195 |
| language | English |
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| physical | XI, 176 S. graph. Darst. |
| publishDate | 1995 |
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| publisher | Springer |
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| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Kogan, Jacob Verfasser aut Robust stability and convexity an introduction Jacob Kogan London u.a. Springer 1995 XI, 176 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 201 Algèbres convexes ram Commande, théorie de la ram Regeltechniek gtt Stabilité ram Control theory Convex domains Stability Konvexität (DE-588)4114284-6 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Robustheit (DE-588)4126481-2 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s DE-604 Dynamisches System (DE-588)4013396-5 s Stabilität (DE-588)4056693-6 s Robustheit (DE-588)4126481-2 s Konvexität (DE-588)4114284-6 s Lecture notes in control and information sciences 201 (DE-604)BV005848579 201 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006601808&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kogan, Jacob Robust stability and convexity an introduction Lecture notes in control and information sciences Algèbres convexes ram Commande, théorie de la ram Regeltechniek gtt Stabilité ram Control theory Convex domains Stability Konvexität (DE-588)4114284-6 gnd Dynamisches System (DE-588)4013396-5 gnd Stabilität (DE-588)4056693-6 gnd Robustheit (DE-588)4126481-2 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| subject_GND | (DE-588)4114284-6 (DE-588)4013396-5 (DE-588)4056693-6 (DE-588)4126481-2 (DE-588)4167992-1 |
| title | Robust stability and convexity an introduction |
| title_auth | Robust stability and convexity an introduction |
| title_exact_search | Robust stability and convexity an introduction |
| title_full | Robust stability and convexity an introduction Jacob Kogan |
| title_fullStr | Robust stability and convexity an introduction Jacob Kogan |
| title_full_unstemmed | Robust stability and convexity an introduction Jacob Kogan |
| title_short | Robust stability and convexity |
| title_sort | robust stability and convexity an introduction |
| title_sub | an introduction |
| topic | Algèbres convexes ram Commande, théorie de la ram Regeltechniek gtt Stabilité ram Control theory Convex domains Stability Konvexität (DE-588)4114284-6 gnd Dynamisches System (DE-588)4013396-5 gnd Stabilität (DE-588)4056693-6 gnd Robustheit (DE-588)4126481-2 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| topic_facet | Algèbres convexes Commande, théorie de la Regeltechniek Stabilité Control theory Convex domains Stability Konvexität Dynamisches System Stabilität Robustheit Ljapunov-Stabilitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006601808&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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