简介:NecessaryandsuffcientconditionsfortheexistenceofaLyapunovfunctionintheLur'eformtoguaranteetheabsolutestabilityofLur'econtrolsystemswithmultiplenon-linearitiesarediscussedinthispaper.Itsimplifiestheexistenceproblemtooneofsolvingasetoflinearmatrixinequalities(LMIs).IfthoseLMIsarefeasible,freeparametersintheLyapunovfunction,suchasthepositivedefinitematrixandthecoefficientsoftheintegralterms,aregivenbythesolutionoftheLMIs.Otherwise,thisLyapunovfunctiondoesnotexist.Somesufficientconditionsarealsoobtainedfortherobustabsolutestabilityofuncertainsystems.Anumericalexampleisprovidedtodemonstratetheeffectivenessoftheproposedmethod.