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S-Variable Approach to LMI-Based Robust Control 2015 ed. [Kõva köide]

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  • Formaat: Hardback, 246 pages, kõrgus x laius: 235x155 mm, kaal: 5685 g, 34 Illustrations, color; 4 Illustrations, black and white; XVII, 246 p. 38 illus., 34 illus. in color., 1 Hardback
  • Sari: Communications and Control Engineering
  • Ilmumisaeg: 05-Nov-2014
  • Kirjastus: Springer London Ltd
  • ISBN-10: 1447166051
  • ISBN-13: 9781447166054
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S-Variable Approach to LMI-Based Robust Control 2015 ed.Suurem pilt
  • Formaat: Hardback, 246 pages, kõrgus x laius: 235x155 mm, kaal: 5685 g, 34 Illustrations, color; 4 Illustrations, black and white; XVII, 246 p. 38 illus., 34 illus. in color., 1 Hardback
  • Sari: Communications and Control Engineering
  • Ilmumisaeg: 05-Nov-2014
  • Kirjastus: Springer London Ltd
  • ISBN-10: 1447166051
  • ISBN-13: 9781447166054
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781447166054.html
Märksõnad:

This book shows how the use of S-variables (SVs) in enhancing the range of problems that can be addressed with the already-versatile linear matrix inequality (LMI) approach to control can, in many cases, be put on a more unified, methodical footing. Beginning with the fundamentals of the SV approach, the text shows how the basic idea can be used for each problem (and when it should not be employed at all). The specific adaptations of the method necessitated by each problem are also detailed. The problems dealt with in the book have the common traits that: analytic closed-form solutions are not available; and LMIs can be applied to produce numerical solutions with a certain amount of conservatism. Typical examples are robustness analysis of linear systems affected by parametric uncertainties and the synthesis of a linear controller satisfying multiple, often conflicting, design specifications. For problems in which LMI methods produce conservative results, the SV approach is shown to achieve greater accuracy.

The authors emphasize the simplicity and easy comprehensibility of the SV approach and show how it can be implemented in programs without difficulty so that its power becomes readily apparent. The S-variable Approach to LMI-based Robust Control is a useful reference for academic control researchers, applied mathematicians and graduate students interested in LMI methods and convex optimization and will also be of considerable assistance to practising control engineers faced with problems of conservatism in their systems and controllers.

1 Introduction
1(8)
1.1 On the Origin and History of S-Variable Approach
1(2)
1.2 On the Denomination S-Variable LMI
3(3)
1.3 Other Denominations Used in Existing Literature
6(1)
1.4 Overview of Selected Topics
6(3)
References
7(2)
2 Robust Performance Analysis of LTI Systems
9(52)
2.1 Introduction
9(1)
2.2 Robust Stability Analysis of Uncertain LTI Systems
9(5)
2.3 Robust Stability Analysis Using S-Variable Approach
14(5)
2.4 Lemmas for SV-LMI Derivation
19(4)
2.5 SV-LMI Results for Robust Performance Analysis Problems
23(22)
2.5.1 Robust Regional Pole Location Analysis
24(8)
2.5.2 Robust H2 Performance Analysis
32(5)
2.5.3 Robust H∞ Performance Analysis
37(4)
2.5.4 Robust Impulse-to-Peak Performance Analysis
41(4)
2.6 Numerical Examples
45(14)
2.6.1 Quarter-Car Suspension Example
45(3)
2.6.2 Stability of Randomly Generated Examples
48(11)
2.7 Conclusions
59(2)
References
59(2)
3 Descriptor Case and System Augmentation
61(46)
3.1 Robust Stability of Systems in Descriptor Form
61(12)
3.1.1 Systems in Descriptor Form
61(2)
3.1.2 Stability
63(3)
3.1.3 Uncertain Descriptor Systems
66(2)
3.1.4 S-Variable Results for Robust Stability
68(2)
3.1.5 Performances
70(3)
3.2 Reducing Size of SV-LMIs
73(5)
3.2.1 Removing Parameter Independent Rows
73(2)
3.2.2 Removing Some Parameter Independent Columns
75(3)
3.3 System Augmentation and Conservatism Reduction
78(13)
3.3.1 Source of Conservatism
78(2)
3.3.2 Preliminary Discussions About Conservatism Reduction
80(3)
3.3.3 Robust Stability
83(4)
3.3.4 Regional Finite Pole Location
87(1)
3.3.5 L2 - induced Norm Performance
88(3)
3.4 Exactness Verification
91(4)
3.5 Numerical Examples
95(9)
3.5.1 Quarter-Car Suspension Example
95(2)
3.5.2 Randomly Generated Examples
97(2)
3.5.3 Satellite Example
99(5)
3.6 Conclusion
104(3)
References
105(2)
4 Robust State-Feedback Synthesis for LTI Systems
107(32)
4.1 Introduction
107(1)
4.2 Preliminaries
107(2)
4.3 Stabilization of Discrete-Time Systems
109(6)
4.3.1 Recursive and Variational Representations
109(2)
4.3.2 LMIs for Stabilization
111(2)
4.3.3 More LMIs Parameterized by Schur Stable Matrices
113(1)
4.3.4 Conclusions on the State-Feedback Stabilization of Discrete-Time Systems
114(1)
4.4 The Continuous-Time Case
115(2)
4.4.1 LMIs Parameterized by Hurwitz Stable Matrices
115(1)
4.4.2 An Unsolved Issue
116(1)
4.5 Pole Location in Subregions of the Complex Plane
117(9)
4.5.1 The Multiperformance Pole Location Problem
117(1)
4.5.2 LMIs Parameterized by a Matrix Pencil
118(3)
4.5.3 LMIs for Pole Location in Convex Regions
121(1)
4.5.4 Pole Location in Intersections of Regions
122(2)
4.5.5 Heuristic Algorithms
124(2)
4.6 Numerical Examples on Quarter-Car Suspension Model
126(10)
4.6.1 Intersection of Interiors of Two Discs
126(4)
4.6.2 Intersection of the Interior of a Disc and Exterior of Another
130(2)
4.6.3 Intersection of a Disc and of a Half Plane
132(4)
4.7 Conclusion
136(3)
References
137(2)
5 Multiobjective Controller Synthesis for LTI Systems
139(26)
5.1 Introduction
139(1)
5.2 Multiobjective Controller Synthesis for Discrete-Time LTI Systems
140(1)
5.3 Basic Results for Discrete-Time System Analysis
141(2)
5.4 State-Feedback Multiobjective H2/H∞ Controller Synthesis
143(3)
5.5 Output-Feedback Multiobjective H2/H∞ Controller Synthesis
146(8)
5.5.1 Linearizing Change of Variables for Standard LMIs
146(2)
5.5.2 Linearizing Change of Variables for SV-LMIs
148(1)
5.5.3 LMIs for Output-Feedback H2 and H∞ Controller Synthesis
149(4)
5.5.4 Advantages of SV-LMIs for Output-Feedback Multiobjective H2/H∞ Controller Synthesis
153(1)
5.6 Numerical Examples
154(10)
5.7 Conclusion
164(1)
References
164(1)
6 Static Output-Feedback Synthesis
165(34)
6.1 Introduction
165(1)
6.2 A New Parametrization for Stabilizing SOF Synthesis
166(7)
6.2.1 Statement of the Problem
166(1)
6.2.2 Parametrization of K SOF
166(3)
6.2.3 Related Parametrizations
169(4)
6.3 H∞ and H2 SOF Synthesis
173(7)
6.3.1 Statement of the SOF Performance Synthesis Problem
173(1)
6.3.2 H2 Optimal Synthesis via SOF
174(5)
6.3.3 H∞ Optimal Synthesis via SOF
179(1)
6.4 SOF Synthesis Under Uncertainties
180(9)
6.4.1 Problem Statement and Preliminaries
180(2)
6.4.2 Robust and Quadratic Stabilization via SOF
182(3)
6.4.3 Robust H2 Suboptimal Control via SOF
185(1)
6.4.4 Quadratic Robust Suboptimal H2 SOF Synthesis
186(3)
6.5 Numerical Procedures
189(3)
6.5.1 Hit-and-Run Synthesis Techniques for Stabilization
189(1)
6.5.2 Two LMI/Randomized Algorithms for SOF Stabilization
190(2)
6.6 Numerical Examples
192(7)
6.6.1 Results from the COMPleib Library
192(2)
6.6.2 Examples with Uncertainties
194(3)
References
197(2)
7 Robust Performance Analysis of Discrete-Time Periodic Systems
199(30)
7.1 Introduction
199(1)
7.2 Stability Analysis of Linear Periodic Systems
199(8)
7.2.1 Definition and Basic Results
199(2)
7.2.2 Robust Stability Analysis Using SV-LMIs
201(6)
7.3 H2 Performance Analysis of Linear Periodic Systems
207(9)
7.3.1 Lifting-Based Treatment
207(1)
7.3.2 Definition of H2 Norm and Basic Results
208(2)
7.3.3 Robust H2 Performance Analysis Using SV-LMIs
210(6)
7.4 H∞ Performance Analysis of Linear Periodic Systems
216(6)
7.4.1 Definition and Basic Results
216(2)
7.4.2 Robust H∞ Performance Analysis Using SV-LMIs
218(4)
7.5 Numerical Examples
222(7)
7.5.1 Robust Stability Analysis
223(1)
7.5.2 Robust H∞ Performance Analysis
224(2)
References
226(3)
8 Robust Controller Synthesis of Periodic Discrete-Time Systems
229(16)
8.1 Introduction
229(1)
8.2 Dual System
230(1)
8.3 Stabilizing Periodic State-Feedback Controller Synthesis
231(4)
8.3.1 Basic Results
231(2)
8.3.2 Robust Stabilizing Controller Synthesis Using SV-LMIs
233(1)
8.3.3 Difficulties in Controller Synthesis Using Rectangular SVs
234(1)
8.4 H2 Controller Synthesis for Linear Periodic Systems
235(3)
8.4.1 Basic Results
235(1)
8.4.2 Robust H2 Controller Synthesis Using SV-LMI
236(2)
8.5 H∞ Controller Synthesis for Linear Periodic Systems
238(2)
8.5.1 Basic Results
238(1)
8.5.2 Robust H∞ Controller Synthesis Using SV-LMI
238(2)
8.6 Numerical Examples
240(5)
8.6.1 Robust Stabilizing Controller Synthesis
241(1)
8.6.2 Robust H2 Controller Synthesis
242(1)
8.6.3 Robust H∞ Controller Synthesis
243(1)
References
244(1)
Index 245
Yoshio Ebihara was born in Fukuoka, Japan on 12th May 1974. He received the D.E. degree in electrical engineering from Kyoto University in 2002. Since 2002 he has been in the Department of Electrical Engineering at Kyoto University where he was made an Associate Professor in 2010. He was the recipient of the 2002 American Control Conference Best Student Paper award and the SICE Annual Conference 2009 International Award. Born in in Leningrad, 2nd March 1974, Dimitri Peaucelle received his PhD from the Paul Sabatier University, Toulouse, France in July 2000. He is now a CNRS researcher at the Laboratory for Analysis and Systems Architecture. He is currently a member of the IFAC Technical Committee on Robust Control, the head of the CNRS working group on methods and tools for robust analysis and control design and Scientific Secretary of the Scientific Council of the CNRS Information and Engineering Department. He was the organizer of the 2006 IFAC ROCOND Symposium and is the NOC Chair of the IFAC 2017 World Congress Steering Committee.