Lyapunov矩陣方程及其擴展方程的數(shù)值求解.pdf

1、上海大學(xué)碩士學(xué)位論文Lyapunov矩陣方程及其擴展方程的數(shù)值求解姓名：張馬彪申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：賀國強20070301AbstractLyapunovmatrixequationplaysaveryimportantroleincontroltheorytommunicationsanddynamicsystemWeusuallydetectsystembasedonthesolutionstothestabil

2、itycontrollabilityandobservabilityInmanycasesweneedlargematrixequationsolution，butundernormalcircumstancesitisdifficulttoachieveaccuratesolutionTherefore，wecanonlyapproximatenumericalmethodtoseeksolutionsFindaprojectionm

3、atrixthroughKrylovsubspacetocarryonmodelreductionThus，asmallscalecontrolsystemiscontainedThisstudyintroducesseveralnewnumericalmethodstosolvetwotypesofmatrixequation11anewmethodforthediscretematrixequationA7XA—X=QThisite

4、rativemethodiscalledKroneckeplotiterationInadditiontousingexistingdecompositionmethodforsolvingtheequation，wealsouse，andthemethodisadefiniteimprovementComparedtomethod，theimprovedmethodhasreducedtheamountofcalculationand

5、memoryMoreoverthismethodhasafasterconvergenceratethanotheriterativemethods2)thecontinuousexpansionofthematrixequationA7P‘PA一2aP‘Q=0AnumberofstandardmethodsareusuallyappliedforhisequationWewillconsiderusingthefollowingmet

6、hodstosolve：(1)decompositionmethod(2)eigenvaluedecom—positionmethod，ifAischaracterizedbydecompositonfactor(3)methodsFirst，KroneckerProductiterativemethodofdiscreteLyapunovequationisrequiredfordiscreteLyapunovequationKron

7、eckerproducttransformationThenitconstructsaconvergeneeofiterativesequenceusingthetransformedepuationThismethodisrelativelyfastcomparedwithotheriterativemethodsofconvergencerateSimultaneitywecarrythroughsomenumericalexper