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1、Automatica48(2012)2951–2955ContentslistsavailableatSciVerseScienceDirectAutomaticajournalhomepage:www.elsevier.com/locate/automaticaBriefpaperAnewclassofLyapunovfunctionsfortheconstrainedstabilizationof✩linearsystemsAldoBalestrino,AndreaCaiti,SergioG
2、rammatico1DepartmentofEnergyandSystemsEngineering,UniversityofPisa,LargoLucioLazzarino1,I-56122Pisa,ItalyarticleinfoabstractArticlehistory:Theconstrainedstabilizationoflinearuncertainsystemsisinvestigatedviatheset-theoreticframeworkReceived13March201
3、1ofcontrolLyapunovR-functions.AnovelcompositionruleallowsthedesignofacompositecontrolReceivedinrevisedformLyapunovfunctionwithexternallevelsetthatexactlyshapesthemaximalcontrolledinvariantsetand24April2012innersublevelsetsarbitrarilyclosetoanychoiceo
4、fsmoothones,generalizingbothpolyhedralandAccepted15June2012truncatedellipsoidalcontrolLyapunovfunctions.ThefeasibilitytestoftheproposedsmoothcontrolAvailableonline19July2012Lyapunovfunctionscanbecastintomatrixinequalitiesconditions.Theconstrainedline
5、arquadraticcontrolisaddressedasanapplication.Keywords:©2012ElsevierLtd.Allrightsreserved.GeneratedLyapunovfunctionsLyapunovmethodsFeedbackstabilizationConstraintsUncertainlinearsystems1.Introductionofthemaximalcontrolledinvariantregionwithareducednum
6、berofparameters(O’Dell&Misawa,2002).InThibodeauetal.(2009)aThestate-feedbackstabilizationofconstraineduncertainlin-linearstate-feedbackcontrolisdesignedbysolvingaBilinearMa-earsystems,coveringsaturationsofthecontrolinputs,statecon-trixInequality(BMI)
7、,maximizingthevolumeoftheestimatedcon-straintsandmodeluncertainties,isequivalenttothedesignofatrolledinvariantset.robustControlLyapunovFunction(CLF).SincetheparticularchoiceThemaincontributionofthispaperisthedefinitionofaofthecandidateCLFalsoprovides
8、anestimationofthecontrollednovelcompositionruleformergingtwodifferentCLFs,allowinginvariantset(Blanchini,1999),theexactsolutionconsistsinpro-thedesignofanon-homotheticsmoothCLFwiththefollowingvidingthelargestcontrolledinvariantregionofthestatespace,a
