鲁棒控制命令

ucomplexCreatesuncertaincomplexscalar.创建不确定性复数标量A=ucomplex(‘NAME’,NOMINAL)createsanuncertaincomplex-valuedparameterranginginthediskofradius1（半径为1）centeredatthevalueNOMINAL.ThestringNAMEspecifiestheparameternameandthecomplexscalarNOMINALspecifiesitsnominalvalue.TheresultingobjectAisofclass"ucomplex".A=ucomplex(‘NAME’,NOMINAL,'Radius',R)specifiesthemaximumdeviationR(说明了最大偏差值)fromthenominalvalue(radiusoftheuncertaintydisk).ThedefaultvalueisR=1.（默认值为1）A=ucomplex(‘NAME’,NOMINAL,'Percentage',P)specifiesthemaximumpercentagedeviationPfromthenominalvalue.ThecorrespondingabsolutedeviationisR=(P/100)*abs(NOMINAL).Usethe"Radius"or"Percentage"propertyofAtoquerytheabsolutepercentageuncertaintyonA.Inaddition,usethe"Mode"propertytospecifywhichuncertaintymeasure(radiusorpercentage)remainsinvariantwhenchangingthenominalvalue.Forexample,ifA.Mode='Percentage',thenachangeinnominalvaluehasnoeffectonA.PercentagebutchangesA.Radius.Notethat"Mode"isinitializedbasedonhowyouspecifytheuncertaintylevel,forexample,A=ucomplex('a',-2+4i,'Radius',2)initializesA.Modeto'Radius'whileA=ucomplex('a',-2+4i,'Percentage',5)initializesA.Modeto'Percentage'.Example:（例子）%Createacomplexparameter'delta'with50%uncertaintyaroundits%nominalvalue-2+3i:a=ucomplex('delta',-2+3i,'Percentage',50);%Theparameterdeltarangesinadiskcenteredat-2+3iwithradius%R=0.5*abs(-2+3i)~1.803:R=a.RadiusBlocksimplificationlevel[{'basic'}|'off'|'full'].Thispropertycontrolshowexpressionsinvolvinguncertainblocksaresimplified.Itsdefaultvalueis'basic',whichmeanselementarysimplificationmethodsareappliedaftereacharithmeticorinterconnectionoperation.Othervaluesare'off'(nosimplificationperformed)and'full'(model-reduction-liketechniquesareapplied)urealCreatesuncertainrealscalar.%创建不确定性实数标量A=ureal(NAME,NOMINAL)createsanuncertainrealparameterrangingintheinterval[NOMINAL-1,NOMINAL+1].ThestringNAMEspecifiestheparameternameandthescalarNOMINALspecifiesitsnominalvalue.TheresultingobjectAisofclass"ureal".%没有说明，默认间隔是1A=ureal(NAME,NOMINAL,'PlusMinus',[-DL,DR])createsanuncertainparametertakingvaluesintheinterval%间隔[NOMINAL-DL,NOMINAL+DR].ThedeviationsDLandDRmustbepositivescalars.Whentheintervaliscenteredatthenominalvalue(DL=DR),youcanspecifytheuncertaintylevelwithasinglevalue,forexample,A=ureal('a',2,'PlusMinus',1.5)%2+/-1.5A=ureal(NAME,NOMINAL,'Range',[LOW,HIGH])specifiestheuncertaintylevelasaninterval[LOW,HIGH].Thenominalvalueshouldlieinthisinterval.%实数值的变化范围A=ureal(NAME,NOMINAL,'Percentage',[-PL,PR])specifiestheuncertaintylevelaspercentagedeviationsfromthenominalvalue:%百分比PL=100*|1-LOW/NOMINAL|,PR=100*|1-HIGH/NOMINAL|WhenPL=PR,youcanspecifythepercentageuncertaintywithasinglevalue,forexample,A=ureal('a',2,'Percentage',10)%2+/-10%Usethe"Range","PlusMinus",or"Percentage"propertiesofAtoquerytheuncertaintylevelasaninterval,absolutedeviation,orpercentagedeviation.Inaddition,usethe"Mode"propertytospecifywhichofthesethreeuncertaintyquantificationsisindependentofthenominalvalue.Forexample,ifA.Mode='Range',thenchangingthenominalvaluehasnoeffectonA.RangebutaffectsbothA.PlusMinusandA.Percentage.Notethat"Mode"isinitializedbasedonhowyouspecifytheuncertaintylevel,forexample,A=ureal('a',2)initializesA.Modeto'PlusMinus'whileA=ureal('a',1,'Percentage',[-1020])initializesA.Modeto'Percentage'.Examples:%实例%Createaurealwithname'a'andnominalvalue4:a=ureal('a',4);%Thedefaultuncertaintyrangeis4plus/minus1:变化范围为3到5a.PlusMinus%Thecorrespondingpercentageuncertaintyisplus/minus25%:a.Percentage%Createaurealwithname'b',nominalvalue5,andrange[26].b=ureal('b',5,'Range',[26]);%Notethat"Mode"isautomaticallysetto'Range':b.Mode%Createaurealwitha25%uncertaintycenteredaroundthe%nominalvalue:c=ureal('c',4,'Percentage',25);%Thecorrespondingintervalis[3,5]:c.Range%Tomodifythenominalvalueto4.5whileretainingthesame[3,5]%range,force"Mode"to'Range'andthensetthenominalvalue:c.Mode='Range'c.NominalValue=4.5Blocksimplificationlevel[{'basic'}|'off'|'full'].Thispropertycontrolshowexpressionsinvolvinguncertainblocksaresimplified.Itsdefaultvalueis'basic',whichmeanselementarysimplificationmethodsareappliedaftereacharithmeticorinterconnectionoperation.Othervaluesare'off'(nosimplificationperformed)and'full'(model-reduction-liketechniquesareapplied).ucomplexmCreatesuncertaincomplexmatrix.%创建一个复数值的矩阵A=ucomplexm(NAME,NOMINAL)createsanuncertaincomplex-valuedmatrixAtakingvaluesinaunitbal（单位圆，圆心为thenominalvalue）centeredatthenominalvalueNOMINAL.Moreprecisely,A=NOMINAL+DELTAwhereDELTAcanbeanycomplex-valuedmatrixsatisfyingnorm(DELTA)<=1.%DELTA为任何一个复数值的矩阵，其满足范数小于或等于1的条件ThestringNAMEspecifiestheuncertainmatrixname.TheresultingobjectAisofclass@ucomplexm.%需要加单引号A=ucomplexm(NAME,NOMINAL,'WL',WL,'WR',WR)createsanuncertaincomplex-valuedmatrixoftheformA=NOMINAL+WL*DELTA*WRwhereDELTAcanbeanycomplex-valuedmatrixsatisfyingnorm(DELTA)<=1.%矩阵范数小于或等于1TheweigthingmatricesWLandWRmustbeinvertibleandtheirdefaultvalueareidentitymatrices.%WL和WR是权重矩阵，而且可逆Example:%Createanuncertaincomplexmatrix"F"withnominalvalue[123i;056]%andweightingmatricesWL=diag([.1.3])andWR=diag([.4.81.2]):F=ucomplexm('F',[123i;056],...'WL',diag([.1.3]),...'WR',diag([.4.81.2]));umatConvertsstaticmodeltouncertainmatrix.%把静态模型转换为不确定性矩阵UM=umat(M)convertsthestaticmodelMtoanuncertainmatrix.AllblocksinMthatdonotrepresentuncertaintyarereplaceduncertainmatrices.Uncertainmatrices(umat)arerationalexpressionsinvolvinguncertainparametersoftypeUREAL,UCOMPLEX,orUCOMPLEXM.Theycanbeusedforworst-casegainanalysisandareusefulforbuildinguncertainstate-spacemodels(seeUSS).Therearetwowaystocreateumatobjects.1.Createuncertainelementsandcombinethem:p=ureal('p',1);M=[0p;1p^2]Misa2-by-2uncertainmatrix(umatobject).2.Convertdoublearraystoumattype:M=umat(1)HereMisa1-by-1matrix(umatobject)withnouncertainty.Uncertainstatespacemodels.%不确定状态空间模型Uncertainstate-spacemodels(uss)arisewhencombiningordinaryLTImodels(seeNUMLTI)withuncertainelements(seeUNCERTAINBLOCK).ussmodelskeeptrackofhowtheuncertainelementsinteractwiththefixeddynamics.Theycanbeusedforrobuststabilityandworst-caseperformanceanalysis.Therearethreewaystoconstructaussobject:1.UseSStocreateuncertainstate-spacemodelsfromuncertainmatricesA,B,C,D(seeUMAT):p=ureal('p',1);A=[03*p;-pp^2];B=[0;p];C=ones(2);D=zeros(2,1);usys=ss(A,B,C,D)TheresultingmodelUSYSisussanddependsontheuncertainparameterp.2.CombinenumericLTImodelswithuncertainelements:sys=tf(1,[11]);k=ureal('k',1);D=ultidyn('Delta',[11]);usys=k*sys*(1+0.1*D)3.ConvertadoublearrayornumericLTImodeltouss:M=tf(1,[111]);usys=uss(M)Here,USYSisaussobjectwithtwostatesandnouncertainty.UncertainFRDmodels.%不确定性UFRD模型UncertainFrequencyResponseDatamodels(ufrd)arisewhencombiningordinaryFRDmodels(seeFRD)withuncertainelements(seeUNCERTAINBLOCK).ufrdmodelskeeptrackofhowtheuncertainelementsaffectthefrequencyresponse.Theycanbeusedforrobuststabilityandworst-caseperformanceanalysis.Therearethreewaystoconstructaufrdobject:1.CombineFRDmodelswithuncertainelements:sys=frd(rand(100,1),logspace(-2,2,100));k=ureal('k',1);D=ultidyn('Delta',[11]);usys=k*sys*(1+0.1*D)2.ConvertaUSSmodeltoufrd:a=ureal('a',1,'range',[0.51.8]);usys=tf(a,[1a]);freqs=logspace(-2,2,100);usys=ufrd(usys,freqs)SeeInputOutputModel/ufrdfordetailsontheconversionsyntax.3.UseFRDtocreateaufrdmodelfromuncertainresponsedata(seeUMAT):RespData=rand(1,1,100)*ureal('delta',1,'percent',50);usys=frd(RespData,logspace(-2,2,100),0.1)usample-Generaterandomsamplesofuncertainvariables%随机采样不确定性变量samples=usample(uvars,N)generatesNrandomsamplesoftheuncertainvariablesinuvars.samples=usample(uvars,N)samples=usample(uvars)samples=usample(uvars,N,Wmax)Example1Generaterandomsamplesofuncertainvariables:%Createastructurethatcontainsuncertainvariablesaand%b.uvars=struct('a',ureal('a',5),'b',ultidyn('b',[23],'Bound',7))%Useusampletogeneraterandomvaluesofaandb.samples=usample(uvars)ufind-FinduncertainvariablesinSimulinkmodeluvars=ufind('mdl')findsUncertainStateSpaceblocksintheSimulinkmodelmdl.uvars=ufind('mdl')[uvars,pathinfo]=ufind('mdl')uvars=ufind(usys_1,usys_2,...)usubs-SubstitutegivenvaluesforuncertainelementsofuncertainobjectsThisMATLABfunctionsetstheelementsinM,identifiedbyElementName1,ElementName2,etc.,tothevaluesinvalue1,value2,etc.B=usubs(M,ElementName1,value1,ElementName2,value2,...)B=usubs(M,S)B=usubs(M,...,'-once')B=usubs(M,...,'-batch')uvars=ufind('mdl')findsUncertainStateSpaceblocksintheSimulink®modelmdl.ItreturnsastructureuvarsthatcontainsalluncertainvariablesassociatedwiththeUncertainStateSpaceblocks.Eachuncertainvariableisaurealorultidynobjectandislistedbynameinuvars.[uvars,pathinfo]=ufind('mdl')returnsacellarraypathinfothatcontainspathstotheUncertainStateSpaceblocksandthecorrespondinguncertainvariablesintheblock.Thefirstcolumnofpathinfoliststheblockpathsthroughthemodelhierarchyandthesecondcolumnliststheuncertainvariablesassociatedwiththeblock.UsepathinfotoverifythatallUncertainStateSpaceblocksinthemodelmdlhavebeenidentified.uvars=ufind(usys_1,usys_2,...)collectsalluncertainvariablesreferencedbytheuncertainmodelusys_n.usys_ncanbeussorufrdmodels.Usethissyntaxasanalternativetoqueryingthemodelitself,whenyouknowtheuncertainmodelsthattheUncertainStateSpaceblocksuse.ufindcanfindUncertainStateSpaceblocksinsideMaskedSubsystems,LibraryLinks,andModelReferencesbutnotinsideAcceleratedModelReferences.ufinderrorsoutifthesameuncertainvariablenamehasdifferentdefinitionsinthemodel.Forexample,ifyourmodelcontainstwoUncertainStateSpaceblockswheretheuncertainsystemvariablesdefinethesameuncertainvariable'unc_par"asultidyn('unc_par',[11])andureal('unc_par',5),suchanerroroccursgridureal-GridurealparametersuniformlyovertheirrangeThisMATLABfunctionsubstitutesNuniformly-spacedsamplesoftheuncertainrealparametersinA.B=gridureal(A,N)[B,SampleValues]=gridureal(A,N)[B,SampleValues]=gridureal(A,NAMES,N)[B,SampleValues]=gridureal(A,NAMES1,N1,NAMES2,N2,...)rss-GeneraterandomcontinuoustestmodelThisMATLABfunctiongeneratesann-thordermodelwithoneinputandoneoutputandreturnsthemodelinthestate-spaceobjectsys.rss(n)rss(n,p)rss(n,p,m,s1,...,sn)rss(n)generatesann-thordermodelwithoneinputandoneoutput%单输入单输出andreturnsthemodelinthestate-spaceobjectsys.Thepolesofsysarerandomandstablewiththepossibleexceptionofpolesats=0(integrators).rss(n,p)generatesan%状态变量个数nthordermodelwithoneinputandpoutputs%一个输入p个输出,andrss(n,p,m)generatesann-thordermodelwithminputsandpoutputs%m个输入和p个输出.Theoutputsysisalwaysastate-spacemodel.rss(n,p,m,s1,...,sn)generatesans1-by-...-by-snarrayofn-thorderstate-spacemodelswithminputsandpoutputs.sys=rss(3,2,2)%ObtainarandomcontinuousLTImodelwiththreestates,twoinputs,andtwooutputsbytypinga=x1x2x3x1-0.541750.097290.08304x20.09729-0.894910.58707x30.083040.58707-1.95271b=u1u2x1-0.88844-2.41459x20-0.69435x3-0.07162-1.39139c=x1x2x3y10.329650.147180y20.59854-0.101440.02805d=u1u2y1-0.87631-0.32758y200Continuous-timesystem.sysic-BuildinterconnectionsofcertainanduncertainmatricesandsystemsThisMATLABfunctionrequiresthat3variableswithfixednamesbepresentinthecallingworkspace:systemnames,inputvarandoutputvar.ultidynCreatesuncertainlineartime-invariantblock.%创建不确定性线性时不变模块UH=ultidyn(NAME,IOSIZE)createsablockUHthatrepresentsarbitrarylineartime-invariant(LTI)dynamicswithfrequencyresponsegainnolargerthanone.Youcanusethisblocktorepresentunmodeleddynamicsorquantifyfrequencyresponseuncertainty.ThestringNAMEandthe1-by-2vectorIOSIZEspecifytheblocknameandI/Osize.Forexample,dH=ultidyn('DeltaH',[23])modelstheuncertaintyonatwo-output,three-inputsystemH(s)asamaximumunit-gaindeviationfromthenominalfrequencyresponse.Tomodelfrequency-dependentuncertaintylevels,multiplytheultidynblockbyasuitable"shaping"filter.Forexample,W=tf([1.1],[.11])dH=W*dHspecifiesanuncertaintyboundthatincreasesfrom0.1atlowfrequenciesto10athighfrequencies.UH=ultidyn(NAME,IOSIZE,'Bound',MAXGAIN)specifiesthemaximumgainoftheuncertaindynamics(thedefaultvalueisMAXGAIN=1).%默认值是1UH=ultidyn(NAME,IOSIZE,'Type','PositiveReal','Bound',BND)specifiesdynamicuncertaintywhosefrequencyresponseliesinthehalf-plane%频域响应在正复半平面UH(jw)+UH(jw)'>=2*BNDThedefaultTYPEis'GainBounded'(uniformboundonthefrequencyresponsegain).The"AutoSimplify"propertycontrolshowexpressionsinvolvinguncertainblocksaresimplified,type"helpultidyn.AutoSimplify"fordetails.WhensamplingtheuncertaindynamicswithUSAMPLE,usethe"SampleStateDim"propertytocontrolhowmanystateseachsampleLTImodelhas(thedefaultvalueis1).Examples:%CreateaMIMOprocessmodelwith20%uncertaintyinitsfrequency%response:Pnom=rss(5,3,4);%5states,3outputs,4inputs%Add20%multiplicativeuncertaintytotheinputofPP=Pnom*(eye(4)+ultidyn('DeltaP',[44],'Bound',0.2))bodemag-BodemagnituderesponseofLTImodelsThisMATLABfunctionplotsthemagnitudeofthefrequencyresponseofthedynamicsystemmodelsys(Bodeplotwithoutthephasediagram).bodemag(sys)bodemag(sys,{wmin,wmax})bodemag(sys,w)bodemag(sys1,sys2,...,sysN,w)bodemag(sys)plotsthemagnitudeofthefrequencyresponseofthedynamicsystemmodelsys(Bodeplotwithoutthephasediagram).Thefrequencyrangeandnumberofpointsarechosenautomatically.bodemag(sys,{wmin,wmax})drawsthemagnitudeplotforfrequenciesbetweenwminandwmax(inrad/TimeUnit,whereTimeUnitisthetimeunitsoftheinputdynamicsystem,specifiedintheTimeUnitpropertyofsys).bodemag(sys,w)usestheuser-suppliedvectorWoffrequencies,inrad/TimeUnit,atwhichthefrequencyresponseistobeevaluated.bodemag(sys1,sys2,...,sysN,w)showsthefrequencyresponsemagnitudeofseveralmodelssys1,sys2,...,sysNonasingleplot.Thefrequencyvectorwisoptional.Youcanalsospecifyacolor,linestyle,andmarkerforeachmodel.Forexample:bodemag(sys1,'r',sys2,'y--',sys3,'gx')ginput-GraphicalinputfrommouseorcursorThisMATLABfunctionenablesyoutoidentifynpointsfromthecurrentaxesandreturnstheirx-andy-coordinatesinthexandycolumnvectors.[x,y]=ginput(n)[x,y]=ginput[x,y,button]=ginput(...)[x,y]=ginput(n)enablesyoutoidentifynpointsfromthecurrentaxesandreturnstheirx-andy-coordinatesinthexandycolumnvectors.PresstheReturnkeytoterminatetheinputbeforeenteringnpoints.[x,y]=ginputgathersanunlimitednumberofpointsuntilyoupresstheReturnkey.[x,y,button]=ginput(...)returnsthex-coordinates,they-coordinates,andthebuttonorkeydesignation.buttonisavectorofintegersindicatingwhichmousebuttonsyoupressed(1forleft,2formiddle,3forright),orASCIInumbersindicatingwhichkeysonthekeyboardyoupressed.fitmagfrd-Fitfrequencyresponsemagnitudedatawithminimum-phasestate-spacemodelusinglog-ChebychevmagnitudedesignThisMATLABfunctionisastable,minimum-phasessobject,withstate-dimensionN%阶数,whosefrequencyresponsemagnitudecloselymatchesthemagnitudedatainA.B=fitmagfrd(A,N)B=fitmagfrd(A,N,RD)B=fitmagfrd(A,N,RD,WT)B=fitmagfrd(A,N,RD,WT,C)B=fitmagfrd(A,N)isastable,minimum-phasessobject,withstate-dimensionN,whosefrequencyresponsemagnitudecloselymatchesthemagnitudedatainA.Aisa1-by-1frdobject,andNisanonnegativeinteger.B=fitmagfrd(A,N,RD)forcestherelativedegreeofBtobeRD.RDmustbeanonnegativeintegerwhosedefaultvalueis0.YoucanspecifythedefaultvalueforRDbysettingRDtoanemptymatrix.B=fitmagfrd(A,N,RD,WT)usesthemagnitudeofWTtoweighttheoptimizationfitcriteria.WTcanbeadouble,ssorfrd.IfWTisascalar,thenitisusedtoweightallentriesoftheerrorcriteria(A-B).IfWTisavector,itmustbethesamesizeasA,andeachindividualentryofWTactsasaweightingfunctiononthecorrespondingentryof(A-B).ThedefaultvalueforWTis1,andyoucanspecifyitbysettingWTtoanemptymatrix.B=fitmagfrd(A,N,RD,WT,C)enforcesadditionalmagnitudeconstraintsonB,specifiedbythevaluesofC.LowerBoundandC.UpperBound.Thesecanbeempty,doubleorfrd(withC.FrequencyequaltoA.Frequency).IfC.LowerBoundisnon-empty,thenthemagnitudeofBisconstrainedtolieaboveC.LowerBound.NolowerboundisenforcedatfrequencieswhereC.LowerBoundisequalto-inf.Similarly,theUpperBoundfieldcanbeusedtospecifyanupperboundonthemagnitudeofB.IfCisadoubleorfrd(withC.FrequencyequaltoA.Frequency),thentheupperandlowerboundconstraintsonBaretakendirectlyfromAas:ifC(w)==–1,thenenforceabs(B(w))<=abs(A(w))ifC(w)==1,thenenforceabs(B(w))>=abs(A(w))ifC(w)==0,thennoadditionalconstraint例子：Fitthemagnitudedatawithaminimum-phase,stablethird-ordersystem.ord=3;b1=fitmagfrd(sysg,ord);b1g=frd(b1,omega);bodemag(sysg,'r',b1g,'k:');legend('Data','3rdorderfit');Fitthemagnitudedatawithathird-ordersystemconstrainedtoliebelowandabovethegivendata.C2.UpperBound=sysg;C2.LowerBound=[];b2=fitmagfrd(sysg,ord,[],[],C2);b2g=frd(b2,omega);C3.UpperBound=[];C3.LowerBound=sysg;b3=fitmagfrd(sysg,ord,[],[],C3);b3g=frd(b3,omega);bodemag(sysg,'r',b1g,'k:',b2g,'b-.',b3g,'m--')legend('Data','3rdorderfit','3rdorderfit,belowdata',...'3rdorderfit,abovedata')Fitthemagnitudedatawithasecond-ordersystemconstrainedtoliebelowandabovethegivendata.ord=2;阶数为2C2.UpperBound=sysg;C2.LowerBound=[];b2=fitmagfrd(sysg,ord,[],sysg,C2);b2g=frd(b2,omega);C3.UpperBound=[];C3.LowerBound=sysg;b3=fitmagfrd(sysg,ord,[],sysg,C3);b3g=frd(b3,omega);bgp=fitfrd(genphase(sysg),ord);bgpg=frd(bgp,omega);bodemag(sysg,'r',b1g,'k:',b2g,'b-.',b3g,'m--',bgpg,'r--')legend('Data','3rdorderfit','2dorderfit,belowdata',...'2ndorderfit,abovedata','bgpg')makeweight1stordersystemwithgivenDCgain,crossoverfrequency,andhighfrequencygain.%创建一个一阶系统（包含低频范围内的误差和误差达到1时的频率，以及在高频时的误差）G=makeweight(DC,CROSSW,HF)createsastable,1st-ordercontinuoustimestate-spacesystemG.ThefrequencyresponseofGsatisfiesG(j*0)=DC,|G(j*CROSSW)|=1,andG(j*infty)=HF.Itmustbethat|DC|<1<|HF|,or|HF|<1<|DC|.G=makeweight(DC,CROSSW,HF,TS)createsastable,1st-orderdiscretetimestate-spacesystemG,withsample-timeTS.ThefrequencyresponseofGsatisfiesG(exp(j*0*TS))=DC,|G(exp(j*CROSSW*TS))|=1,andG(exp(j*PI))=HF.CROSSW*TSmustbelessthanPI.Inbothcontinuous-timeanddiscrete-time,thelowfrequencyandhighfrequencytargetsmustsatisfy|DC|<1<|HF|,or|HF|<1<|DC|.robuststab-Calculaterobuststabilitymarginsofuncertainmultivariablesystem%计算多变量不确定性系统的鲁棒稳定性裕度/裕量Anominallystableuncertainsystemisgenerallyunstableforspecificvaluesofitsuncertainelements.[stabmarg,destabunc,report,info]=robuststab(sys)[stabmarg,destabunc,report,info]=robuststab(sys,opt)Anominallystableuncertainsystemisgenerallyunstableforspecificvaluesofitsuncertainelements.Determiningthevaluesoftheuncertainelementsclosesttotheirnominalvaluesforwhichinstabilityoccursisarobuststabilitycalculation.Iftheuncertainsystemisstableforallvaluesofuncertainelementswithintheirallowableranges(rangesforureal,normboundorpositive-realconstraintforultidyn,radiusforucomplex,weightedballforucomplexm),theuncertainsystemisrobustlystable.Conversely,ifthereisacombinationofelementvaluesthatcauseinstability,andallliewithintheirallowableranges,thentheuncertainsystemisnotrobustlystablerobuststabcomputesthemarginofstabilityrobustnessforanuncertainsystem.Astabilityrobustnessmargingreaterthan1meansthattheuncertainsystemisstableforallvaluesofitsmodeleduncertainty.Astabilityrobustnessmarginlessthan1impliesthatcertainallowablevaluesoftheuncertainelements,withintheirspecifiedranges,leadtoinstability.Numerically,amarginof0.5(forexample)impliestwothings:theuncertainsystemremainsstableforallvaluesofuncertainelementsthatarelessthan0.5normalizedunitsawayfromtheirnominalvaluesand,thereisacollectionofuncertainelementsthatarelessthanorequalto0.5normalizedunitsawayfromtheirnominalvaluesthatresultsininstability.Similarly,amarginof1.3impliesthattheuncertainsystemremainsstableforallvaluesofuncertainelementsupto30%outsidetheirmodeleduncertainranges.Seeactual2normalizedforconvertingbetweenactualandnormalizeddeviationsfromthenominalvalueofanuncertainelement.Aswithotheruncertain-systemanalysistools,onlyboundsontheexactstabilitymarginarecomputed.TheexactrobuststabilitymarginisguaranteedtolieinbetweentheseupperandlowerboundsBasicSyntaxSupposesysisaufrdorusswithMuncertainelements.Theresultsof[stabmarg,destabunc,Report]=robuststab(sys)arethatstabmargisastructurewiththefollowingfieldsFieldDescriptionLowerBound%Lowerboundonstabilitymargin,positivescalar.Ifgreaterthan1,thentheuncertainsystemisguaranteedstableforallvaluesofthemodeleduncertainty.Ifthenominalvalueoftheuncertainsystemisunstable,thenstabmarg.UpperBoundandstabmarg.LowerBoundbothequal0.UpperBound%Upperboundonstabilitymargin,positivescalar.Iflessthan1,theuncertainsystemisnotstableforallvaluesofthemodeleduncertainty.%上限值小于1，则系统不是鲁棒稳定的DestabilizingFrequency%Thecriticalvalueoffrequencyatwhichinstabilityoccurs,withuncertainelementsclosesttotheirnominalvalues.Ataparticularvalueofuncertainelements(seedestabuncbelow),thepolesmigrateacrossthestabilityboundary(imaginary-axisincontinuous-timesystems,unit-diskindiscrete-timesystems)atthefrequencygivenbyDestabilizingFrequency.%不稳定频率，和上界相对应destabuncisastructure%结构体ofvaluesofuncertainelements,closesttonominal,thatcauseinstability.ThereareMfieldnames,whicharethenamesofuncertainelementsofsys.Thevalueofeachfieldisthecorrespondingvalueoftheuncertainelement,suchthatwhenjointlycombined,leadtoinstability.Thecommandpole(usubs(sys,destabunc))showstheinstability.IfAisanuncertainelementofsys,thenactual2normalized(destabunc.A,sys.Uncertainty.A)willbelessthanorequaltoUpperBound,andforatleastoneuncertainelementofsys,thisnormalizeddistancewillbeequaltoUpperBound,provingthatUpperBoundisindeedanupperboundontherobuststabilitymargin.Reportisatextdescriptionoftheargumentsreturnedbyrobuststab.Ifsysisanarrayofuncertainmodels,theoutputsarestructarrayswhoseentriescorrespondtoeachmodelinthearray.lftdata-Decomposeuncertainobjectsintofixednormalizedandfixeduncertainparts%把不确定性结构体分解称为固定的标称模型和固定的不确定性部分ThisMATLABfunctionseparatestheuncertainobjectAintoacertainobjectMandanormalizeduncertainmatrixDeltasuchthatAisequaltolft(Delta,M),asshownbelow.[M,Delta]=lftdata(A)[M,Delta]=lftdata(A,List)[M,DELTA,BLKSTRUCT]=lftdata(A)[M,DELTA,BLKSTRUCT,NORMUNC]=lftdata(A)lftdatadecomposesanuncertainobjectintoafixedcertainpartandanormalizeduncertainpart.lftdatacanalsopartiallydecomposeanuncertainobjectintoanuncertainpartandanormalizeduncertainpart.Uncertainobjects(umat,ufrd,uss)arerepresentedascertain(i.e.,not-uncertain)objectsinfeedbackwithblock-diagonalconcatenationsofuncertainelements.[M,Delta]=lftdata(A)separatestheuncertainobjectAintoacertainobjectMandanormalizeduncertainmatrixDelta%一个不确定性矩阵suchthatAisequaltolft(Delta,M),asshownbelow.IfAisaumat,thenM