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1、4IEEETRANSACTIONSONAUTOMATICCONTROL,VOL.AC-26,NO.1,FEBRUARY1981MultivariableFeedbackDesign:ConceptsforaClassicaVModernSynthesisJOHNC.DOYLEANDGUNTERSTEIN,MEMBER,IEEEAbstmei--lhispaperpresentsapracticaldesignperspectiveonmulti-oftheclassicalBodegain/phaseconstraints151
2、,[6]whichvariablefeedbackcontrolproblem.Itreviewsthebasicissue-feedbacklimitultimateperformanceoffeedbackinthefaceofsuchdesigninthefaceofuncertainties-andgeneralizesknownsingle-input,uncertainties.SeveralproposedMIMOdesignproceduressingleoutput(SISO)statementsandcons
3、traintsofthedesignproblemtoareexaminednextinthecontextofthefundamentalmultiinpat,multioutput("0)cases.Twomajor"0designapproachesarethenevaluatedinthecontextoftheseresults.feedbackdesignissue.TheseincludetherecentfrequencydomaininverseNyquistarray(INA)andcharacteristi
4、cloci(CL)methodsandthewell-knownlinear-quadraticI.INTRODUCTIONGaussian(LQG)procedure.TheINAandCLmethodsarefoundtobeeffective,butonlyinspecialcases,whileHElasttwodecadeshavebroughtmajordevelop-LQGmethods,ifusedproperly,havedesirablegeneralTmentsinthemathematicaltheory
5、ofmultivariablefeatures.Thelatterarefortunateconsequencesoflineartimeinvariantfeedbacksystems.Theseincludethequadraticoptimization,notexplicitlysoughtafterortestedcelebratedstatespaceconceptforsystemdescriptionandforbythetheoreticaldevelopersoftheprocedure.Practi-the
6、notionsofmathematicaloptimizationforcontrollertionersshouldfindthemvaluablefordesign.synthesis[I],[2].Varioustime-domain-basedanalyticalandcomputationaltoolshavebeenmadepossibleby11.FEEDBACKFUNDAMENTALStheseideas.Thedevelopmentsalsoincludecertaingener-alizationsoffre
7、quency-domainconceptswhichofferanal-Wewilldealwiththestandardfeedbackconfigurationysisandsynthesistoolsintheclassicalsingle-input,single-illustratedinFig.1.Itconsistsoftheinterconnectedplantoutput(SISO)tradition[3],[4].Unfortunately,however,(G)andcontroller(K)forcedb
8、ycommands(r),mea-thetwodecadeshavealsobroughtagrowingschismsurementnoise(v),anddisturbances(d).Thedashedbetweenpractitionersoffeedb
