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1、FuzzySetsandSystems45(1992)135-156135North-HollandStabilityanalysisanddesignoffuzzycontrolsystemsKazuoTanakaandMichioSugenoDepartmentofSystemsScience,TokyoInstituteofTechnology,4259Nagatsuta,Midori-ku,Yokohama227,JapanReceivedNovember1989RevisedMay1990Abstract:Thestabilityanalysisandth
2、edesigntechniqueoffuzzycontrolsystemsusingfuzzyblockdiagramsarediscussed.First,weshowtheconceptoffuzzyblocksandconsidertheconnectionproblemsoffuzzyblocksdiagrams.Wederivesometheoremsandcorollarieswithrespecttotwobasictypesofconnectionsoffuzzyblocks.Inordertopreservesomepropertiesinacon
3、nectionoffuzzyblocks,continuouspiecewise-polynomialmembershipfunctionsaredefined.Secondly,asufficientconditionwhichguaranteesthestabilityoffuzzysystemsisobtainedintermsofLyapunov'sdirectmethod.Wegiveanimportantfactbasedonthiscondition.Thirdly,weproposeanewdesigntechniqueofafuzzycontrol
4、ler.Thefuzzyblockdiagramsandthestabilityanalysisareappliedtothedesignproblemsofamodel-basedfuzzycontroller.Keywords:Controltheory;model-basedcontroller;fuzzycontrolsystems;fuzzyblockdiagrams;continuouspiecewise-polynomialmembershipfunction;stabilityanalysis;Lyapunov'sdirectmethod.1.Int
5、roductionRecently,fuzzycontrolhasbeenappliedtomanypracticalindustrialapplications.Frommis-cellaneousapplications,wecanseethatfuzzycontrolhasthefollowingadvantages:(1)realizationofmulti-objectivecontrol;(2)realizationofexpertcontrol;(3)realizationofrobustcontrol.Ontheotherhand,asoneofth
6、edisadvantagesoffuzzycontrol,itissaidthatatpresentwelackanalyticaltoolsforfuzzycontrolsystems.Inotherwords,weneedafuzzysystemstheorylikelinearsystemstheory.Weconsiderthreeimportantconceptsconcerningtheestablishmentofafuzzysystemstheory:(C1)theconnectionproblemsoffuzzyblockdiagrams;(C2)
7、thestabilityanalysisoffuzzycontrolsystems;(C3)thenewdesigntechniqueofafuzzycontroller.Inthelinearcase,blockdiagramswhicharerepresentedbytransferfunctionsareutilizedintheanalysisoflinearcontrolsystems.Similarly,wecananalyzefuzzycontrolsystemsifwehavetheconceptsoffuzzyblockdiagramswhic
