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1、6%LINEAROPTIMALCONTROLTHEORYFORDISCRETE-TIMESYSTEMS6.1INTRODUCTIONInthefirstfivechaptersofthisbook,wetreatedinconsiderabledetaillinearcontroltheoryforcontinuous-timesystems.Inthischapterwegiveacon-densedreviewofthesametheoryfordiscrete-timesystems.Sincethetheoryoflineardiscrete-timesystemsveryclo
2、selyparallelsthetheoryoflinearcon-tinuous-timesystems,manyoftheresultsaresimilar.Forthisreasonthecommentsinthetextarebrief,exceptinthosecaseswheretheresultsfordiscrete-timesystemsdeviatemarkedlyfromthecontinuous-timesituation.Forthesamereasonmanyproofsareomitted.Discrete-timesystemscanbeclassifie
3、dintotwotypes:1.Inherentlydiscrete-timesystems,suchasdigitalcomputers,digitalfiiters,monetarysystems,andinventorysystems.Insuchsystemsitmakessensetoconsiderthesystematdiscreteinstantsoftimeonly,andwhathappensinbetweenisirrelevant.2.Discrete-timesystemsthatresultfromconsideringcontinuous-limesyste
4、msatdiscreteinstantsoftimeonly.Thismaybedoneforreasonsofconvenience(e.g.,whenanalyzingacontinuous-timesystemonadigitalcomputer),ormayarisenaturallywhenthecontinuous-timesystemisinterconnectedwithinherentlydiscrete-timesystems(suchasdigitalcontrollersordigitalprocesscontrolcomputers).Discrete-time
5、linearoptimalcontroltheoryisofFeatinterestbecauseofitsapplicationincomputercontrol.6.2THEORYOFLINEARDISCRETE-TIMESYSTEMS6.2.1IntroductionInthissectionthetheoryoflineardiscrete-timesystemsisbrieflyreviewed.ThesectionisorganizedalongthelinesofChapter1.Manyoftheresultsstatedinthissectionaremoreexten
6、sivelydiscussedbyFreeman(1965).,4426.2LincorDiscrete-TimcSystems4436.2.2StateDescriptionofLinearDiscrete-TimeSystemsItsometimeshappensthatwhendealingwithaphysicalsystemitisrelevantnottoobservethesystembehavioratallinstantsoftimetbutonlyatasequenceofinstants/,,i=0,1,2,....Ofteninsuchcasesitispossi
7、bletocharacterizethesystembehaviorbyquantitiesdefinedatthoseinstantsonly.Forsuchsystemsthenaturalequivalentofthestatedifferentialequationisthestatefiiierer~ceeqttationx(i+1)=f[x(i),u(i),i],6-1wherex(i)isthestateandu(i)
