向量值函数连续与可导的关系

20056222()JournalofGuaniTaCherSEduGiouUniversity(NaaiscienFtion)Jun.2005Vol.22No.2:10028743(2005)02001004,,,(,fll253023):,X,.:;();();:0177.1:AX,X.Xx(t)()(),,.J~S,Banach().Banach,James,,.1()1x(t)DKX,(1)x(t)tD,fX,}x(t)flx(t)(2)x(t)tD,lim{}x(t)x(t)}}=0;(3)x(t)D(),,x(t)D().1x(t)tD,t..:x(t)0,1](l)e,,t=0,tt[0,1,(n=1,2,!||t,X,,~,~,_~_,,,~..e,n/l1,U.,,xLt)xU)=8,(t~0).llx()_=1n1,Z,),:xLtx(O)=8,(t0).,x(t),,,.:x(t)O,co)(12)x(t)=(t.,,;,1+tZ1+:21+:,),x(t)0,co),t=O.:20041227:(1965),,,,.2,,,:2()2GK,tG,x(t)GX,(:):,ex,-,h)x,xx(t),x(t)t().x(t)G(),G().2x(t)Gt,t,.2.:x(t)[2]:(1,1)~z,1nno,||!l|,ZX1nx(t)x(0)t{e,,t()x(t)x(0)_0,,t0,x(0)O,0,11n(x(1/n)x(0))!!1,xt0.:x(t),,,[3]:x(t)0,co)(12),!,(,~,(,l(*2)(vI),),0tco,,x(t)[0,co),,((,,1+:,),,t=0.33x(t)(0t1)BanachX,O,O,0,1(a,,b;)a*)(,aZ,2),,(a,,),(-}}[()x(a)!},f=1(1)x(t).,3,l,x(b)x(a)}(1),x(:).,.34.3x(t)Gto,t.3.:x(t)0,1z,()22tn1,=,n1,,.o,r,teo,1]rll!K|l|,.rX,x(t)t=0.,Ilx(t}0,tte0,1,x(t)1,,,t,,:,0,=0,(t~0).,(l)(m),,f0=(1,1,1,)e(m),,x(1/n)x(0):10L=l,=,,.;,=0,t1/n,t[0,1,x(t)t=O..:x(t)0,212,X,(n:,,,,,,0:27r,01,x(t)0,2.,,,!,,,()2,x(t),t0,2,tt0,2,}lx(+:)x(:)}l=sinn(t+t)sinnt~.2=nL,2tZ~0,(t~0)_,t.t2,x(t)0,2.,()=,x(t)={x,(t)}t,{x,(t)}.,,}},(:)}}={x(:){+co(2),,,,,.2,cosnt2_cont_1nInnCOSznt,lx(t0)!co,(2),(t)[0,24x(t).4..:x(t)0,1]L0,1,x(t)]()=1,0t0,t((1(3),x(t)0,1,[4],.,Pa,[o,1,}}[x()()[x(a)()}}{a,,[o,1,),0,,,),11)a)}}*,x(t)0,1.,2,,,:x(t)]()x(t)]()0min(t,t){!tl,min(,)max(:,,),,.,,nU,1CUJ||LttoO,max(t,t)((1,x(t)t,t~tLO,1O,;)()d,(,,x(t)tO,1,.,[s].(3),,x(t)0,13.,(L0,1)Lco0,lj,L0,1],f=b(L0,1,,X(:){;X(:):()()d:;()d:,:o,t0,lj,(,X:,,,,x(t)[0,1y(t)L[0,1Lco0,1,(4)t[0,1,,f=b(d,,JLxt)J)UL,,(:));,(:)(:)()d:,(5)(4)(5),f=b()L[0,1,{;,(:,(,(,d(t0,1],(6)te0,1,y=t)(1),(6)L0,{;,(:)(:)d:(:,,v(,L0,b(CO,1,{;,(:),d,(7),.,C0,1]z+(t),t1/k,t1(t),t,t+1/kO,[0,1(=n,n+1,21|11.we/ŽZ.,,nt1/n,t+1/n[0,1,(7)1(!;()*(:)d:{,(:),d:,(*-1,,ly(t)},,x(t)O,1].().:1.M.:,1984,2].M.:,1994.3,.J.,2003,19(6):45.[2222()22RobustStabilizationofaClassofLinearNeutralSystemswithNonlinearPerturbationSCLNJing,MOYuzhong,YuJiminDepartmentofMathematiesandCmputerSeienee,LiuzhouTeachers11ege,Liuzhou545004,ChinaAbstract:Inthispaperrobuststabilizationofaelassoflinearneutralsystemswithnonlinearperturba-tion15diseussedusingthemethedofLIM.01conditionthatnonlinearuneertainfunetionsareunded,wefirstderiveasuffieientconditionforrobuststabilityindependentofdel.Then,weprovidesuffieientcon-ditionsfordesigningamemorylessstate-feedbaekcontrOller,whichstabilizestheuneertainneutralsystem.Keywos:LIM;timedelaysystem;uneertain;robuststability:[13]4.J].,2001(2):6266.5],.machJ].,19%,11(3):329333.TheRelationofContinuityandDerivativeaboutVeCtorvaluedFunetionIXNGLihua,LIUDeiin,JIAODeie,LlNa(DepartmentofMathematics,Dezhau11e,Dezhou253023,China)Abstraet:Throughconstruetingthereverseexarnples,thisPaPerprovesadequatelythatstrongeonti-nuty15onlyaneeessarycondietionofweakderivativefortheveetorvaluedfunetions.Theveetorvaluedfunctionsexistinthattheyarestronglyabsolutecontinuity,buttherearenotalmostweakderivativehereandthere.Keywos:veetor-valuedfunetion;strongly(weakly)continuity;strongly(weakly)derivable;strolyabsolutecontinuity:]