Mathematical Control Theory II: Behavioral Systems and Robust Control

259 Pages·2015·4.118 MB·English

by  Madhu N. Belur, M. Kanat Camlibel, Paolo Rapisarda, Jacquelien M.A. Scherpen (eds.)

Lecture Notes in Control and Information Sciences 462
Madhu N. Belur
M. Kanat Camlibel
Paolo Rapisarda
Jacquelien M.A. Scherpen Editors
Mathematical
Control Theory II
Behavioral Systems and Robust Control
Lecture Notes in Control and Information
Sciences
Volume 462
Series editors
Frank Allgöwer, Stuttgart, Germany
Manfred Morari, Zürich, Switzerland
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A. Rantzer, Lund Institute of Technology, Sweden
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More information about this series at http://www.springer.com/series/642
Madhu N. Belur M. Kanat Camlibel
(cid:129)
Paolo Rapisarda Jacquelien M.A. Scherpen
(cid:129)
Editors
Mathematical Control
Theory II
Behavioral Systems and Robust Control
123
Editors
MadhuN.Belur PaoloRapisarda
Department ofElectrical Engineering Department ofElectronics andComputer
Indian Institute of Technology Science
Mumbai University of Southampton
India Southampton
UK
M.Kanat Camlibel
JohannBernoulli Institute for Mathematics Jacquelien M.A. Scherpen
andComputer Science Engineering andTechnologyinstitute
University of Groningen Groningen
Groningen University of Groningen
TheNetherlands Groningen
TheNetherlands
ISSN 0170-8643 ISSN 1610-7411 (electronic)
Lecture Notesin Control andInformation Sciences
ISBN978-3-319-21002-5 ISBN978-3-319-21003-2 (eBook)
DOI 10.1007/978-3-319-21003-2
LibraryofCongressControlNumber:2015942816
Mathematics Subject Classification: 34H05, 34H15, 47N70, 70Q05, 93B05, 93B52, 93C05, 93C10,
93C15,93C35
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Foreword
This volume is offered to Prof. Dr. Harry L. Trentelman in celebration of his
birthday. It contains papers by his collaborators, including a number of former
Ph.D. students and postdoctoral fellows.
This is the second of a series of two books, appearing in connection with the
workshop “Mathematical systems theory: from behaviors to nonlinear control”
dedicatedtothe60thbirthdaysofArjanvanderSchaftandHarryTrentelman,both
attheJohannBernoulliInstituteforMathematicsandComputerScienceandatthe
Jan C. Willems Center for Systems and Control at the University of Groningen.
v
Preface
Imean,whatisanun-birthdaypresent?
Apresentgivenwhenitisn’tyourbirthday,ofcourse.
(L.Carroll,ThroughtheLooking-Glass,
andWhatAliceFoundThere.
ChapterVI:HumptyDumpty)
To those who are familiar with him since many decades, the scientist and human
being Harry L. Trentelman displays a remarkable almost invariance property. For
aslongaswehaveknownhim,theadjectivesthatbestcontinuetodescribeHarry’s
attitude to science and academic work are: resilient, creative, energetic, hard-
working.Whenoneisalmostgivinguptryingtoprovesomeresultandisreadyto
add yet another assumption to make life a bit easier, Harry always comes to the
rescue(typicallythenextmorning,afteranightofhardthinking)withasimpleand
effective solution. In science, Harry is also rigorous, original, open-minded, and
skeptical:wefondlyrecallhisabilitytoshootdownourmostcherishedpettheories
with one sharp question, and his tireless efforts in correcting our sloppiness in
thinking or writing. One should add that Harry has always been the epitome of
scientificintegrity,thathehasconsistentlydisplayedanexcellenttasteinhischoice
of problems and in finding elegant solutions to them, and that he is an ambitious,
kind, helpful, conscientious, and truly educational supervisor to his Master and
Ph.D. students. All these qualities have brought Harry to make pioneering and
lasting scientific contributions to areas as diverse as geometric control theory, the
behavioral approach, and most recently systems over networks. The excellency of
his work has been officially recognized in his recent nomination as IEEE Fellow
and Senior Editor for the IEEE Transactions on Automatic Control.
The adjectives that come to mind when trying to describe his personality are:
charming, sociable, enthusiastic, optimistic, witty. His particular brand of humor
wouldrequirefarbetterwritersthanustobedescribedadequately;sufficeittosay
that nobody who has sat next to him at conference dinners can easily forget his
cheeky,brilliantone-liners.Allofthosewhoknowhimeventangentiallyremember
vii
viii Preface
his outspoken passion for sports and outdoor activities, his appreciation of good
music, his love for and involvement in his family, and his taste for dancing.
Here isa man who loves life so unconditionally as tobe an exampletoall who
meethim.Hedoesnotphilosophiseabouthowtolivelifefully;heshowsonehow
todoitinpractice.Whatthen,onecouldask,doessuchamandeserveasagiftfor
theanniversary ofalmostthreescores yearsofalife? What couldbethebesttoken
of our appreciation for him as a man and a scientist?
As his friends and former students we pondered long over the obvious choices.
A luxurious penthouse in Manhattan? A shiny Lamborghini? A stately Tuscan
villa? After much deliberation we discarded all these options: none was good
enough to really translate our affection for and esteem of Harry (and given his
unswerving devotion to Volvo family cars, he would not have liked the
Lamborghini anyway).
Almostdriventodesperationbyourinabilitytomake ourfeelingsconcrete,we
finallyfoundtheperfectgift:acollectionofscientificpaperswrittenspecificallyfor
thisoccasionbyfriends,colleagues,andformerstudents!Theconfirmationthatthis
was the right idea was the enthusiasm with which it was accepted by the contrib-
utorstothisvolume,whoquicklyproducedthehigh-qualityworksgatheredinthis
volume.
What you are holding in your hands then, Harry, is the best “sixtieth
un-birthday”giftwecouldthinkof.Wepresentittoyouwithaffection,admiration,
and our best wishes for several decades more of top-level scientific productivity.
Mumbai, India Madhu N. Belur
Groningen, The Netherlands M. Kanat Camlibel
Southampton, UK Paolo Rapisarda
Groningen, The Netherlands Jacquelien M.A. Scherpen
May 2015
Contents
1 Open Loop Control of Higher Order Systems . . . . . . . . . . . . . . . 1
Paul A. Fuhrmann and Uwe Helmke
2 Bilinear Differential Forms and the Loewner Framework
for Rational Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
P. Rapisarda and A.C. Antoulas
3 Noninteraction and Triangular Decoupling Using Geometric
Control Theory and Transfer Matrices . . . . . . . . . . . . . . . . . . . . 45
Jacob van der Woude
4 Simultaneous Stabilization Problem in a Behavioral
Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Osamu Kaneko
5 New Properties of ARE Solutions for Strictly Dissipative
and Lossless Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Chayan Bhawal, Sandeep Kumar, Debasattam Pal
and Madhu N. Belur
6 Stochastic Almost Output Synchronization for Time-Varying
Networks of Nonidentical and Non-introspective Agents Under
External Stochastic Disturbances and Disturbances
with Known Frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Meirong Zhang, Anton A. Stoorvogel and Ali Saberi
7 A Characterization of Solutions of the ARE and ARI. . . . . . . . . . 129
A. Sanand Amita Dilip and Harish K. Pillai
8 Implementation of Behavioral Systems. . . . . . . . . . . . . . . . . . . . . 151
Diego Napp and Paula Rocha
ix
x Contents
9 Synchronization of Linear Multi-Agent Systems
with Input Nonlinearities via Dynamic Protocols . . . . . . . . . . . . . 169
Kiyotsugu Takaba
10 Strong Structural Controllability of Networks . . . . . . . . . . . . . . . 183
Nima Monshizadeh
11 Physical Network Systems and Model Reduction . . . . . . . . . . . . . 199
Arjan van der Schaft
12 Interconnections of L2-Behaviors: Lumped Systems . . . . . . . . . . 221
Shiva Shankar
13 On State Observers—Take 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
Jochen Trumpf
14 When Is a Linear Complementarity System Disturbance
Decoupled?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
A.R.F. Everts and M.K. Camlibel