Linear Systems Theory J.P.Hespanha.pdf

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LINEARSYSTEMSTHEORY

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LINEARSYSTEMSTHEORYJO~AOP.HESPANHAPRINCETONUNIVERSITYPRESS~PRINCETONANDOXFORD

Copyrightc�2009byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock,OxfordshireOX201TWAllRightsReservedLibraryofCongressCataloging-in-PublicationDataHespanha,Jo˜aoP.Linearsystemstheory/Jo˜aoP.Hespanha.p.cm.ISBN978-0-691-14021-6(hardcover:alk.paper)1.Linearsystems—Textbooks.2.Systemanalysis—Textbooks.I.TitleQA402.H472009003�.74—dc222009006371BritishLibraryCataloging-in-PublicationDataisavailableThisbookhasbeencomposedinMinionPrintedonacid-freepaper.press.princeton.eduPrintedintheUnitedStatesofAmerica10987654321

TOMYWIFESTACYANDTOOURSONRUI

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CONTENTSPREAMBLExiiiLINEARSYSTEMSI-BASICCONCEPTSISYSTEMREPRESENTATION31STATE-SPACELINEARSYSTEMS51.1State-SpaceLinearSystems51.2BlockDiagrams71.3Exercises102LINEARIZATION112.1State-SpaceNonlinearSystems112.2LocalLinearizationaroundanEquilibriumPoint112.3LocalLinearizationaroundaTrajectory142.4FeedbackLinearization152.5Exercises193CAUSALITY,TIMEINVARIANCE,ANDLINEARITY223.1BasicPropertiesofLTV/LTISystems223.2CharacterizationofAllOutputstoaGivenInput243.3ImpulseResponse253.4LaplaceTransform(review)273.5TransferFunction273.6Discrete-TimeCase283.7AdditionalNotes293.8Exercise304IMPULSERESPONSEANDTRANSFERFUNCTIONOFSTATE-SPACESYSTEMS314.1ImpulseResponseandTransferFunctionforLTISystems314.2Discrete-TimeCase324.3ElementaryRealizationTheory324.4EquivalentState-SpaceSystems364.5LTISystemsinMATLABr�384.6Exercises395SOLUTIONSTOLTVSYSTEMS415.1SolutiontoHomogeneousLinearSystems415.2SolutiontoNonhomogeneousLinearSystems43

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