Tbegoalofthispaperistoresearchonenewcharacteristicofcomplexsystem.Brittleness,whichisonenewcharacteriticofcomplexsystem,ispresentedinthispaper.Thelinguisticandqualitativedescriptionsofcomplexsystemarealsogiveninthispaper.Otherwise,thequalitativedescriptionofcomplexsystemispresentedatfirst.Onthebasisofanalyzingtheexistingbrittlenessproblems,linguisticdescriptionandmathematicdescriptionofbrittlenessaregivenaswell.Threekindsofphenomenatojudgebrittlenessofcomplexsystemarealsogiven,basedoncatastrophetheory.Basiccharacteristicsofbrittlenessaregivenonthebasisofitsmathematicdescription.Twocriticalpointsetsaredefinedbyusingcatastrophetheory.Thedefinitionofbrittlenessanditsrelatedtheorycanservethecontrolofcomplexsystem,andprovidetheoreticalbasisforthedesignandcontrolofcomplexsystem.
