Robust Output Feedback H-infinity Control and Filtering for Uncertain Linear Systems

254 Pages·2014·1.531 MB·English

by  Xiao-Heng Chang

Studies in Systems, Decision and Control 7
Xiao-Heng Chang
Robust Output
Feedback
H-infinity Control
and Filtering
for Uncertain
Linear Systems
Studies in Systems, Decision and Control
Volume 7
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Xiao-Heng Chang
Robust Output Feedback
H-infinity Control
and Filtering for Uncertain
Linear Systems
123
Xiao-Heng Chang
College ofEngineering
Bohai University
Jinzhou
China
ISSN 2198-4182 ISSN 2198-4190 (electronic)
ISBN 978-3-642-55106-2 ISBN 978-3-642-55107-9 (eBook)
DOI 10.1007/978-3-642-55107-9
Springer Heidelberg NewYork Dordrecht London
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(cid:2)Springer-VerlagBerlinHeidelberg2014
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Preface
It is well known that robust H control and filtering are important issues for
1
systems. In recent years, the linear matrix inequality (LMI) technique has been
widely used to solve the robust H control and filtering problems for uncertain
1
linearsystemswithpolytopicuncertainparametersand/ornormboundeduncertain
parameters.
Although a large number of design methods have been developed to deal with
the robust H control and filtering problems for both continuous-time and dis-
1
crete-time uncertain linear systems, the design problem of output feedback H
1
controllerscannotbeformulatedintheframeworkofLMI.Ingeneral,theproblem
can be represented as a bilinear matrix inequality (BMI) problem. However, the
BMI problem is nonconvex and difficult to obtain solution. To obtain LMI-based
conditions for designing output feedback H controllers, some studies have to
1
impose constraints on system matrices. In summary, those results are limited and
cannot be applied to general control systems.
This monograph aims to present some new results on robust output feedback
H control and filtering for uncertain linear systems. It lists an LMI decoupling
1
approach, and the main results of this monograph are expressed in a unified LMI
framework,whichwillprovideaneffectivefoundationforthefutureresearch.Itis
primarilyintendedforgraduatestudentsincontrolandfiltering,butcanalsoserve
as a valuable reference material for researchers wishing to explore the area of
control and filtering of linear systems.
The background required of the reader is knowledge of basic control system
theory, basic Lyapunov stability theory, and basic LMI theory.
Jinzhou, China, March 2014 Xiao-Heng Chang
v
Acknowledgments
This monograph would not be possible without the work done in the previous
resultsofothers.Ithankthemfortheirscientificdedicationandespeciallyfortheir
influence on my research and on this monograph. It is a great pleasure to express
mythankstothosewhohavebeeninvolvedinvariousaspectsofresearchleading
to the work.
TheauthorwishestoexpresshisheartygratitudetoadvisorsProf.Guang-Hong
Yang and Prof. Yuanwei Jing, Northeastern University, China, for directing the
research interest of the author to the general area of controls. Special thanks to
Prof. QinglingZhang,Northeastern University,China, for thehelpfulsuggestions
onthismonograph.IwanttothankProf.ShengyuanXuattheNanjingUniversity
of Science and Technology, China, Prof. Shaocheng Tong at the Liaoning
University of Technology, China, and Prof. Bing Chen at Qingdao University,
China,forallthehelpinmyacademicresearch.IamalsogratefultoProf.Huijun
Gao, Prof. Zhongdang Yu, and Prof. Shen Yin, Bohai University, China, for the
support and encouragement the author has had during the writing of this
monograph.
Finally,theauthorwouldliketoexpresshisgratitudetotheeditorNaXuatthe
SpringerBeijingOffice.Withouttheirappreciationandhelp,thepublicationofthis
book would have not gone so smoothly.
The monograph was supported in part by the National Natural Science Foun-
dation of China (Grant No. 61104071), by the Program for Liaoning Excellent
TalentsinUniversity,China(GrantNo.LJQ2012095),bytheOpenProgramofthe
Key Laboratory of Manufacturing Industrial Integrated Automation, Shenyang
University, China (Grant No. 1120211415).
vii
Contents
1 Introduction and Preview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Problem Formulation and Preliminaries . . . . . . . . . . . . . . . . . . 4
1.2.1 Output Feedback H Control. . . . . . . . . . . . . . . . . . . . 4
1
1.2.2 H Filtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1
1.2.3 LMI and Matrix Properties. . . . . . . . . . . . . . . . . . . . . . 6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Robust Static Output Feedback H Control. . . . . . . . . . . . . . . . . 17
‘
2.1 With Time-Invariant Polytopic Uncertainties . . . . . . . . . . . . . . 17
2.1.1 Discrete-Time Systems . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.2 Continuous-Time Systems . . . . . . . . . . . . . . . . . . . . . . 74
2.2 With Norm Bounded Uncertainties . . . . . . . . . . . . . . . . . . . . . 83
2.3 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
2.3.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
2.3.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3 Robust Dynamic Output Feedback H Control. . . . . . . . . . . . . . . 95
‘
3.1 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.2 Basic Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.3 LMI Decoupling Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.4 A Whole Design Strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.5 For the Case DðhÞ6¼0 and HðhÞ6¼0. . . . . . . . . . . . . . . . . . . . 120
3.6 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4 Robust Observer-Based Output Feedback H Control . . . . . . . . . 125
‘
4.1 With Time-Invariant Polytopic Uncertainties . . . . . . . . . . . . . . 125
4.1.1 Condition A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.1.2 Condition B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
ix
x Contents
4.2 With Time-Varying Norm Bounded Uncertainties. . . . . . . . . . . 135
4.2.1 The Two-Step Process with a Selection. . . . . . . . . . . . . 135
4.2.2 A Simple LMI Result . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.2.3 LMI Decoupling Approach. . . . . . . . . . . . . . . . . . . . . . 145
4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5 Robust H Filtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
‘
5.1 Discrete-Time System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.1.1 H Performance Analysis . . . . . . . . . . . . . . . . . . . . . . 156
1
5.1.2 Robust H Filters Design . . . . . . . . . . . . . . . . . . . . . . 160
1
5.1.3 LMI Decoupling Approach. . . . . . . . . . . . . . . . . . . . . . 174
5.2 Continuous-Time Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.2.1 H Performance Analysis . . . . . . . . . . . . . . . . . . . . . . 177
1
5.2.2 Robust H Filters Design . . . . . . . . . . . . . . . . . . . . . . 181
1
5.3 Numerical Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
6 With Other Types of Uncertainties. . . . . . . . . . . . . . . . . . . . . . . . 191
6.1 With Feedback Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 191
6.1.1 Robust Output Feedback H Control . . . . . . . . . . . . . . 191
1
6.1.2 Robust H Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . 200
1
6.1.3 Output Feedback Non-fragile H
1
Control with Type III . . . . . . . . . . . . . . . . . . . . . . . . . 211
6.1.4 Non-fragile H Filtering with Type I and Type II . . . . . 218
1
6.2 Frobenius Norm Uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . 233
6.2.1 Observer-Based Output Feedback
Non-fragile H Control. . . . . . . . . . . . . . . . . . . . . . . . 234
1
6.2.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Acronyms
LMI Linear matrix inequality
LMIs Linear matrix inequalities
BMI Bilinear matrix inequality
xi