Numerical Linear Algebra in Signals, Systems and Control

495 Pages·2011·5.93 MB·English

by  A. Aricò

Lecture Notes in Electrical Engineering
Volume 80
For furthervolume
http://www.springer.com/series/7818

Paul Van Dooren Shankar P. Bhattacharyya
• •
Raymond H. Chan Vadim Olshevsky
• •
Aurobinda Routray
Editors
Numerical Linear Algebra
in Signals, Systems
and Control
123
Editors
Dr. PaulVanDooren Prof.VadimOlshevsky
CESAME Department of Mathematics
Universite Catholique deLouvain Universityof Connecticut
Batiment Euler 4,avenueGeorges AuditoriumRoad196
Lemaitre Storrs Connecticut
1348LouvainlaNeuve U-906269-3009
Belgium USA
e-mail: [e-mail] e-mail: [e-mail]
Prof.Shankar P.Bhattacharyya Dr. AurobindaRoutray
Department of Electricaland Computer Department of ElectricalEngineering
Engineering Indian Instituteof Technology
Texas A&MUniversity Kharagpur 721302
ZachryEngineering Center India
College Station e-mail: [e-mail]
TX 77843-3128
USA
e-mail: [e-mail]
Prof.Raymond H.Chan
Department of Mathematics
The ChineseUniversity ofHong Kong
Shatin,New Territories,
Hong KongSAR
e-mail: [e-mail]
ISSN 1876-1100 e-ISSN1876-1119
ISBN 978-94-007-0601-9 e-ISBN978-94-007-0602-6
DOI 10.1007/978-94-007-0602-6
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Foreword
A Special Volume Dedicated to Biswa Nath Datta
The Indian Institute of Technology-Kharagpur (IIT-KGP) hosted an international
workshopon‘‘NumericalLinearAlgebrainSignal,Systems,andControl’’,during
January 9–11, 2007. The conference was sponsored by IEEE Kharagpur Section,
Department of Electrical Engineering of IIT-KGP, and Systems Society of India-
IIT Kharagpur Chapter. The convener of the workshop was Professor Aurobinda
Routray of Electrical Engineering Department of IIT-KGP.
The workshop was interdisciplinary in nature blending linear and numerical
linear algebra with control and systems theory, and signal processing. Though a
few such conferences, such as the AMS conference on ‘‘Linear Algebra and its
Role in Systems Theory’’, and a series of four SIAM conferences on ‘‘Linear
Algebra in Signals, Systems, and Control’’, were held before in USA, this is the
firsttimeaninterdisciplinaryconferenceofthistypewasheldinIndia.Aboutone
hundred mathematicians, computational scientists, and engineers from several
countries of the world, including Australia, Belgium, Brazil, Cyprus-Turkey,
Germany,HongKong,India,SriLanka,USA,andVenezuela,participatedinthis
workshop. The picture below shows the group of attendees.
v
vi Foreword
At the banquet of this workshop, Professor Biswa Nath Datta was honored by
the IEEE for his numerous contributions in the area of numerical linear algebra
with control and systems theory, and signal processing. The ceremony was pre-
sidedbyProfessor N.Kishore,the-thenPresidentoftheIEEEKharagpurChapter
and Profressor Rajendra Bhatia, an eminent India mathematician from Indian
Statistical Institute, was the principal banquet speaker. The other speakers were:
the late Gene Golub, Professor of Stanford University, and Professors Paul Van
Dooren of Universi´te Catholique de Louvain, Belgium, Volker Mehrmann of
Technische Universi¨tat Berlin, Germany and V. K. Mohan of Indian Institute of
Technology, Kharagpur, India. It was also decided at the end of this meeting to
dedicate a special volume toBiswa Datta. This volume contains papers presented
at the workshop, as well as contributed and invited papers sent in by authors
workinginthisarea.Allofthesepaperswentthrougharegularrefereeingprocess.
As editors of this volume we are pleased to convey our best wishes to Biswa.
ShankarBhattacharyya,RaymondChan,VadimOlshevsky,AurobindaRoutray
and Paul Van Dooren.
Biosketch of Biswa Nath Datta
BiswaDattawasborninthevillageofBighira,WestBengal,Indiain1941.After
completing his high school education from his village school and bachelor and
masterdegreesfromCalcuttaUniversityinIndia,hemovedtoLondon,Englandto
pursuehishigherstudiesin1967.Primarilyduetoeconomicreasons,hecouldnot
completehisstudiesinLondonandin1968,movedtoHamilton,Ontario,Canada
from where he completed his masters degree in mathematics in 1970.
BasedonhisMastersThesis,writtenunderJosephCsima,hepublishedhisfirst
paper, DAD Theorem for Nonnegative Symmetric Matrices in Journal of Combi-
natorial Theory in 1972.
Foreword vii
He then joined University of Ottawa, Canada and received his Ph.D. degree in
1972, under the direction of the late James H. Howland.
Immediately after his graduation from University of Ottawa, he got married to
Karabi Datta, who at that time was also a fellow graduate student in mathematics
at University of Ottawa and working under the direction of the late Professor
Howland.
Later that year, he met with Air Vice Marshal S. Roychoudhury, the-then
Director of Gas Turbine Research Establishment (GTRE), Bangalore, India, who
was visiting North America at that time with the mission of recruiting ‘‘Indian-
talents’’ from abroad. Mr. Roychoudhury offered both Biswa and Karabi the
positions as scientific officers at GTRE. Additionally, Datta was appointed as the
Head of the Computational Mathematics Group in that organization. They both
enthusiastically went back to India in 1973 with their new positions. Unfortu-
nately, this non-academic government job was not stimulating and challenging
enoughforDattaandhedecidedtoleaveIndiaagain.Afterspendingafewmonths
at Ahmadu Bello University, Zaria, Nigeria, as a lecturer (1974) and about four
years (1975–1980) at State University of Campinas, Campinas, Brazil as an
Associate Professor of Computational Mathematics, he finally moved back to
North America in 1980 as a visiting Associate Professor of Computer Science at
Pennsylvania State University.
Theirtwochildren,RajarshiandRakhi,bothwereborninCampinas,in1976and
1979, respectively. Biswa and Karabi now have two grandsons: Jayen(4) and
Shaan(2)—thier parents are Rajarshi and Swati. Datta joined Northern Illinois
Universityin1981asaFullProfessorinMathematicalSciencesDepartment.Hewas
nominatedbyHansSchneiderandseveralotherprominentmathematiciansforthis
position,Therehe,alongwithsomeofhiscolleagues,developedthecurrentCom-
putationalMathematicsProgramatNIU.Healsoplayedakeyroleintheplanning
anddevelopmentofthePh.D.ProgramintheMathematicalSciencesDepartment.
Healsoservedastheactingdirectorofthe‘‘ApplicationsInvolvementComponent
(AIC)’’ofthePh.D.Programinmathematicalsciencesfrom1993to1996.
In2001,hewasappointedasaPresidentialResearchProfessoratNIUandwas
elevatedtothe position of‘‘Distinguished ResearchProfessor’’in2005,which he
currentlyholds.DattahasalsoheldVisitingProfessorshipatUniversityofIllinois
(1985)andUniversityofCalifornia,SanDiego(1987–1988)andnumerousshort-
term Visiting Professorship (including several Distinguished Visiting Professor-
ship)atinstitutesandresearchorganizationsinvariouscountriesaroundtheworld.
TheseincludeAustralia,Brazil,Chile,China,England,France,HongKong,Greece,
India,Mexico,Malaysia,Portugal,Spain,Taiwan,andVenezuela.
ThoughDattaspentmostofhisacademiccareeroutsideIndia,hemaintaineda
close scientific relationship with India. In1993, hewas appointedas amemberof
overseas panel of scientists for the Council of Scientific and Industrial Research,
Government of India. During 1993–2003, he made many short-term scientific
visits to research laboratories and prominent institutes in India as a scientific
advisor. He also contributed to the development of the scientific software for
India’s first supercomputer ‘‘Param’’.
viii Foreword
In recognition of his contributions to science and engineering, Datta has
receivedseveralawardsandhonors.HewashonoredinaspecialIEEEsponsored
honoring ceremony during the banquet of the International Workshop on
NumericalLinear Algebra inSignals, Systemsand Control, IIT-Kharagpur, 2007,
and more recently, in another honoring ceremony on the occasion of the First
International Conference on Power, Control, Signals and Computations, held at
the Vidya Academy of Science and Technology, Thrissur, India, 2010, where he
was awarded a Gold Medal of Honor. Datta was also recognized by some of the
world’s leading linear and numerical linear algebraists in a special banquet
honoring ceremony held during the IMA sponsored International Conference on
LinearandNumericalLinearAlgebra:Theory,MethodsandApplications,heldat
Northern Illinois University, DeKalb, Illinois, August 12, 2009. Besides these
professional recognitions, Datta has also received several other important
professional awards and honors. He is an IEEE Distinguished Lecturer, an IEEE
Fellow, an Academician ofthe Academy of Nonlinear Sciences, and is a recipient
of NIU’s Presidential Research Professorship, International Federation of
Nonlinear Analysis Medal of Honor, Senior Fulbright Specialist award by US
State Department and several Plaques of Honor awarded by local IEEE chapters
of IIT-Kharagpur, India, and NIU. A special issue on ‘‘Inverse Problems in Sci-
enceandIndustry’’oftheJournalNumericalLinearAlgebrawithApplications
will be published in his honor in 2011.
Datta has versatile research interests ranging from theoretical and computa-
tional linear algebra to control and systems theory and vibration engineering.
• Contributions to inertia, stability, and D-stability
In the early part of his research career, he worked on the stability, inertia, and
D-stability of matrices. He collaborated with several leading matrix theorists,
including DavidCarlson, PaulFuhrmann, CharlesJohnsonandHansSchneider
on this endeavor. In a series of papers published between 1976 and 1980, he
developed an unified matrix theoretic framework, via the historical Lypunov
stabilitytheory,formanyapparentlydiverseclassicalroot-separationresultsfor
polynomials, which were obtained by celebrated mathematicians in the early
twentiethcentury.Intheprocessofdoingso,hederivedsimpleandelementary
matrixtheoreticproofsofseveraloftheseclassicalroot-separationcriteria(e.g.,
proofs of the Routh–Hurwitz–Fujiwara root-separation criterion and stability
criterion of Lienard–Chipart via Bezoutian). Most of the original proofs were
based on function-theory and were too involved and long. A key result proved
by him in this context, was that the Bezoutian of two polynomials is a sym-
metrizer of its associated companion matrix.
In 1979, in a paper published in Numerische Mathematik, he and David
Carlson,developedanumericalalgorithmforcomputingtheinertiaandstability
of a non-hermitian matrix and in 1980, along with David Carlson, and Charles
Johnson, developed a new characterization of D-stability for symmetric tridi-
agonalmatrices.TheconceptofD-stabilityarisingineconomicswasoriginally
formulatedbyNobelLaureate,KennethArrow.Aneffectivecharacterizationof
Foreword ix
D-stabilitystilldoesnotexist.Notably,theirresultisstilloneofthestate-of-the-
art results on this problem in the literature.
• Contributions to Computational Control Theory
Inthelasttwodecades,Dattaandseveralotherprominentresearchers,including
Paul Van Dooren, Alan Laub, Rajni Patel, Andras Varga, Volker Mehrmann,
and Peter Benner, and others have developed computationally effective algo-
rithms for control systems design and analysis using state-of-the-art numerical
linearalgebratechniques.Whilethereexistedahigh-levelmathematicaltheory,
practically applicable algorithms were lacking in this area. These and other
previously existing algorithms have been the basis of one of Datta’s books,
Numerical Methods for Linear Control Systems Design and Analysis and two
software packages, MATHEMATICA based Control Systems Professional-
AdvancedNumericalMethodsandMATLABToolkitMATCONTROL.Dattahas
delivered several invited workshops on Computer-aided Control Systems
Design and Analysis based on this book and the software packages, at some of
the leading IEEE and other conferences and at universities and research orga-
nizations around the world. His work on ‘‘Large-Scale Computations in Con-
trol’’ has been in the forefront of attempts made by him and several others to
develop parallel and high-performance algorithms for control systems design.
HispaperLarge-scaleandParallelComputationsinControl,LAA,1989,isone
oftheearlyresearchpapersinthisarea.Afewotherimportantpapersauthored/
co-authoredbyhiminthisareainclude,ArnoldimethodsforlargeSylvester-like
observer matrix equations and an associated algorithm for partial spectrum
assignment (with Youcef Saad), LAA (1991), A parallel algorithm for Sylves-
ter-observer equation (with Chris Bischof and A. Purkayastha), SIAM Journal
of Scientific Computing (1996), Parallel algorithms for certain matrix compu-
tations (with B. Codenotti and M. Leoncini), Theoretical Computer Science
(1997),ParallelAlgorithmsinControl,Proc.IEEEConf.DecisionandControl
(1991), and High performance computing in control, SIAM book on Parallel
Processing for Scientific Computing (1993). While parallel and high perfor-
mance algorithms were developed in many disciplines in science and engi-
neering, control engineering was lagging behind.
• Contributions to Quadratic Inverse Eigenvalue Problems
The quadratic inverse eigenvalue problem (QIEP) is an emerging topic of
research. Because of intrinsic mathematical difficulties and high computational
complexities, research on QIEP has not been very well developed. Datta, in
collaborationwithseveralvibrationengineers,numericallinearalgebraists,and
optimizationspecialists,includingZ.-J.Bai,MoodyChu,EricChu,SienDeng,
Sylvan Elhay, Abhijit Gupta, Wen-Wei Lin, Yitshak Ram, Marcos Raydan,
Kumar V. Singh, Jesse Prat, Jenn Nan Wang, C.S. Wang, and some of his
former and current students, Sanjoy Brahma, Joao Carvalho, Joali Moreno,
Daniil Sarkissian, and Vadim Sokolov, have made some significant contribu-
tions to the development of numerically effective and practically applicable
algorithms and associated mathematical theory for several important QIEPs