Stability analysis and design of fuzzy control systems.pdf

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1、FuzzySetsandSystems45(1992)135-156135North-HollandStabilityanalysisanddesignoffuzzycontrolsystemsKazuoTanakaandMichioSugenoDepartmentofSystemsScience,TokyoInstituteofTechnology,4259Nagatsuta,Midori-ku,Yokohama227,JapanReceivedNovember1989RevisedMay1990Abstract:Thestabilityanalysisandt

2、hedesigntechniqueoffuzzycontrolsystemsusingfuzzyblockdiagramsarediscussed.First,weshowtheconceptoffuzzyblocksandconsidertheconnectionproblemsoffuzzyblocksdiagrams.Wederivesometheoremsandcorollarieswithrespecttotwobasictypesofconnectionsoffuzzyblocks.Inordertopreservesomepropertiesinac

3、onnectionoffuzzyblocks,continuouspiecewise-polynomialmembershipfunctionsaredefined.Secondly,asufficientconditionwhichguaranteesthestabilityoffuzzysystemsisobtainedintermsofLyapunov'sdirectmethod.Wegiveanimportantfactbasedonthiscondition.Thirdly,weproposeanewdesigntechniqueofafuzzycont

4、roller.Thefuzzyblockdiagramsandthestabilityanalysisareappliedtothedesignproblemsofamodel-basedfuzzycontroller.Keywords:Controltheory;model-basedcontroller;fuzzycontrolsystems;fuzzyblockdiagrams;continuouspiecewise-polynomialmembershipfunction;stabilityanalysis;Lyapunov'sdirectmethod.1

5、.IntroductionRecently,fuzzycontrolhasbeenappliedtomanypracticalindustrialapplications.Frommis-cellaneousapplications,wecanseethatfuzzycontrolhasthefollowingadvantages:(1)realizationofmulti-objectivecontrol;(2)realizationofexpertcontrol;(3)realizationofrobustcontrol.Ontheotherhand,ason

6、eofthedisadvantagesoffuzzycontrol,itissaidthatatpresentwelackanalyticaltoolsforfuzzycontrolsystems.Inotherwords,weneedafuzzysystemstheorylikelinearsystemstheory.Weconsiderthreeimportantconceptsconcerningtheestablishmentofafuzzysystemstheory:(C1)theconnectionproblemsoffuzzyblockdiagram

7、s;(C2)thestabilityanalysisoffuzzycontrolsystems;(C3)thenewdesigntechniqueofafuzzycontroller.Inthelinearcase,blockdiagramswhicharerepresentedbytransferfunctionsareutilizedintheanalysisoflinearcontrolsystems.Similarly,wecananalyzefuzzycontrolsystemsifwehavetheconceptsoffuzzyblockdiagram

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