Table Of ContentDiscrete-Time Linear Systems
Guoxiang Gu
Discrete-Time Linear
Systems
Theory and Design with Applications
123
GuoxiangGu
DepartmentofElectricaland
ComputerEngineering
LouisianaStateUniversity
ElectricalEngineeringBuilding
BatonRouge,LA
USA
ISBN978-1-4614-2280-8 e-ISBN978-1-4614-2281-5
DOI10.1007/978-1-4614-2281-5
SpringerNewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2012930050
©SpringerScience+BusinessMedia,LLC2012
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,
NY10013, USA),except forbrief excerpts inconnection with reviews orscholarly analysis. Usein
connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,
orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.
Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare
notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject
toproprietaryrights.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
To myfamilyandfriends
Preface
Linearsystemtheoryandoptimalestimationandcontrolaretaughtatthegraduate
level in many universities. This book is written primarily for graduate students
in electrical engineering who specialize in control. Yet, the mathematical theory
appliesnotonlytofeedbackcontrolsystemsbutalsotocommunicationandsignal
processing. Indeed, from two decades of my teaching in the advanced digital
control class at LSU, I found that whenever I introduced applications to digital
communications and signal processing such as equalization and precoding, more
graduate students came to attend my class. Teaching of this new application
stimulated more interests from students. Control students were eager to learn
applicationsofcontroltheorytocommunicationsthathadmoreactionsinthehigh-
tech boom time, while students from communication and signal processing saw
thenewprosectofthemathematicalsystemtheoryintheirspecializedarea.These
observationsmotivatedmetoseriouslyconsiderexpansionofmyteachingmaterial
toincludenewapplicationsotherthanfeedbackcontrol.However,itisalsotruethat
controlandcommunicationseldominteractinthelastcentury,inspiteofbeingtwo
ofthemostsuccessfulareasinengineeringsystemdesign.Thetwoareasaremore
orlessisolatedfromeachotherintermsofteachingandresearch.
Two major technological developments, namely, wireless communications and
the Internet, in the last decade have changed the aforementioned isolatory phe-
nomenon. Because of the existence of multipath and fading, the dynamic and
random behaviors of the wireless channel cannot be ignored. And because of the
multiusernatureforInternet,thecommunicationchannelissharedbymorethanone
user. As such, the emergenceof the wireless Internethasbroughtin designissues
for dynamic multivariable communication systems. On the other hand, wireless
communications and Internet have made remote and networked control systems
possible, in which feedbackcontrollersand physicalprocesses are situated in two
different locations and connected via wireless channels or Internet. Therefore,
communication issues also need be addressed in control system design. It is felt
strongly by this author that a unified approach is necessary to design of optimal
MIMO dynamic systems in both control and communications. This text provides
a platform for graduate students and researchers in these two different areas to
vii
viii Preface
study and work together. Such multidisciplinary interactions will greatly benefit
eachotherandfurtheradvancetheresearchfrontierinengineeringsystemdesign.
This text is focused on system and control theory with applications to design
of feedbackcontrolsystemsand the signalprocessingaspectof the design issues.
It is written for the first or second year graduate students, who are interested in
generalareasofcontrol,orcommunications,andsignalprocessing.Thereadersare
assumed to have some basic knowledge on random processes and linear algebra,
and have taken some basic undergraduate courses in discrete-time control, or
digital communications and digital signal processing from electrical engineering.
The appendicesprovidea quickreviewforthe requiredmathematicalbackground
materials. Students are encouraged to read the related texts to strengthen their
backgroundknowledge.
Thisbookconsistsoftwoparts.Thefirstpartpresentslinearsystemtheoryand
theoryofoptimalestimationandoptimalcontrolforlinearsystems. State spaceis
themainsubjectthatprovidesnotonlythemathematicalinsightintothestructureof
linearsystemsbutalsothecomputationaltoolforobtainingthesolutiontooptimal
estimationandoptimalcontrol.Thesecondpartpresentsthedesignmethodologyfor
linearsystemswithfeedbackcontrolanddatacommunicationsasapplicationareas.
The design issues in modeling, system identification, channel estimation, symbol
detectionindatacommunications,anddisturbancerejectioninfeedbackcontrolare
addressedbasedonthetheoriesfromthefirstpart.
It is observed by this author that design has been overlooked for the past two
decadesin engineeringcurriculaatthe graduatelevel.While coursesonadvanced
research topics are important in training graduate students, the lack of design
experienceforgraduatestudentsmayweakenthequalityofourresearchprograms.
This text represents an effort to teach engineering system design at the graduate
level, in hope to bring design into the graduate curriculum. The author welcomes
anycommentsandsuggestionsregardingthematerialsinthistext.
BatonRouge,LA GuoxiangGu
Acknowledgments
In writing this textbook,I receiveda lot of help from many people.The two who
helpedthe mostare JohnBaillieul and Andre´ Tits. Johnallowed me to step down
inthemiddleofthesecondappointmentfromthejobofAssociateEditorforSIAM
Journal for Control and Optimization, while Andre´ reduced my workload as an
AssociateEditorforAutomatica.Bothjournalsarepremiumcontroljournals.Iam
really happy that I have worked with these two extraordinary people. I am also
indebtedtomanyotherpeople,includingRobertBitmead,XirenCao,andPramod
Khargonkar.
Istartedwritingthisbookmorethan7yearsago.Manyofmygraduatestudents
read its early drafts and helped me to revise and polish the book. Among them,
I especially want to mention Jianqiang He, whose valuable inputs are crucial for
improvingthecontentsofthebook.OthergraduatestudentsincludeHeshemBadr,
EhabBadran,LijuanLi,andZhongshanWu,whosePh.D.dissertationscontribute
tothistextbookinvariousforms.
I would like to thank Jie Chen, Li Qiu, and Kemin Zhou for the long-lasting
friendshipovertwodecades.Theirhelpandencouragementareextremelyvaluable
tome.Inaddition,myfamilyhasputupwithmewithgreatpatience.Mychildren
actuallylearnedhowtohaveweekendswithoutme.
Finally, I would like to thank Steve Elliot, Merry Stuber, and Alison Waldron
fromSpringerwhohelpedtospeedupthewritingofthisbook.
ix
