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1、Vol.35,No.11ACTAAUTOMATICASINICANovember,2009OptimalStateEstimationforDiscrete-timeSystemswithRandomObservationDelays11HANChun-YanZHANGHuan-ShuiAbstractThispaperinvestigatesthelinearminimummeansquareerrorstateestimationfordiscrete-timesystemswithMarkovjumpdelays.Inordertosolvetheoptimalestimati
2、onproblem,thesingleMarkovdelayedmeasurementisrewrittenasanequivalentmeasurementwithmultipleconstantdelays,thenadelay-freeMarkovjumplinearsystemisobtainedviastateaugmentation.TheestimatorisderivedonthebasisofthegeometricargumentsintheHilbertspace,andarecursiveequationofthe¯lterisobtainedbysolvin
3、gtheRiccatiequations.Itisshownthattheproposedstateestimatorisexponentiallystableunderstandardassumptions.KeywordsLinearestimation,discrete-timesystems,Markovjumpdelays,RiccatiequationInmanysignalestimationproblems,itisusuallyas-formulatedasanoptimallinear¯lterofaclassofMarkovsumedthattheobserva
4、tionpacketsarereceivedeitherim-jumplinearsystemsviastateaugmentation[11¡15].A¯nite-[1¡2]mediatelyorwithaconstantandknowndelay.How-dimensionalrecursive¯lterisobtainedintermsofRiccatiever,incertainnewengineeringapplications,theobserva-di®erenceequations.Wealsoshowthattheestimatoristionpacketsneed
5、tobetransmittedthroughacommunica-stableunderstandardassumptions.tionnetworkwhichmayinduceconsiderableandrandomlyTherestofthispaperisorganizedasfollows.Section1varyingtransmissiondelays.Examplesareo®eredbycom-introducesthesystemunderconsideration.Theminimumplexnetworkedsensorsystemscontainingala
6、rgenumbervariancestateestimatorispresentedinSection2,anditsoflowpowersensors,aswellascomplexdynamicalpro-stabilityisstudiedinSection3,whichrequiresmostofourcesseslikeadvancedaircraft,spacecraft,andmanufactur-e®orts.InSection4,anumericalexampleispresentedtoingprocess,wheretimedivisionmultiplexed
7、networksareillustratethemainresults.Finally,someconclusionsareemployedforexchangeofinformationbetweenspatiallydis-drawninSection5.tributedplantcomponents.Allthesenewengineeringap-Notations.Thenotationinthispaperisfairlystan-nplica
