Control and Analysis of Pulse-Modulated Systems
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(287) x =?=?= 8. . . 5. y } 2^xB>@:XDMO}.}}.}.}}.}.}}.}.}.}}.}.}}.}.}}.}.}}.}.}}.}.}.}}.} B>@:XDMRGcGHB<NB H WRCE<S[CXtUvCSS[C \HL<1<SNBWNa=?E] }}.}.}}.}.}}.}.}.}}.} QBL[ML<[\HG J +QPH∞M.L<[M : !ZGC EIWRCEKiM S<[M S(}.}}.}.}}.}.}}.}.}}.}.}.}}.} 8 }? ZEEHM S1XDCKC: }}.}.}}.}.}}.}.}.}}.}.}}.}.}}.}.}}.}.}}.}.}.}}.} 8 }~# ;\<[M S1XDCKC: }.}.}}.}.}}.}.}.}}.}.}}.}.}}.}.}}.}.}}.}.}.}}.} 8 }~y 2^x:dM S=?>OM EK<[L }.}}.}.}}.}.}.}}.}.}}.}.}}.}.}}.}.}}.}.}.}}.} QBL[ML<[\HG Jm# +QPHM.L<[M : !9\:lWRCEKi M S<[M S }.}.}}.}.}}.}.}}.}.}}.}.}.}}.} ZEEHM S1XDCKC: }}.}.}}.}.}}.}.}.}}.}.}}.}.}}.}.}}.}.}}.}.}.}}.} }? ;\<[M S1XDCKC: }.}.}}.}.}}.}.}.}}.}.}}.}.}}.}.}}.}.}}.}.}.}}.} }~# 2^x:dM S=?>OM EK<[L }.}}.}.}}.}.}.}}.}.}}.}.}}.}.}}.}.}}.}.}.}}.} }~y 4CEHW X?\HL=DCEHL }}.}.}}.}.}}.}.}}.}.}.}}.}.}}.}.}}.}.}}.}.}}.}.}.}}.} M"UqM S[M EHWRMRLm}.}}.}.}}.}.}}.}.}}.}.}.}}.}.}}.}.}}.}.}}.}.}}.}.}.}}.}. K5 _8 _8y _8 _88 _85 _85 # # y 5.
(288)
(289) QPHM<PHMRL=DL WRCEHL=DGM S[L4WRCEK<S[CX BEHG|BETBX?J L=DLg:S[C XDM >OLQBL[LNC W =pB<[MRG =?<P`:\XDL[M"!9>OCKG \XpB<[M_G LJ L<[M >OL_}{$EO<P=DLgL[MRW <=DCE 4M1]=?i MB S=DM"UY=?EK<S[CKG \HW <=DCE`<[C.:\XDL[M1>OCKG \XpB<=DCE/ =?<P|B.L:dM"! W =pBXdUvCKW \HLQCEm:\XDL[M"&! =DG <Ph>OCKG \XpB<=DCEY}g UvM f:SNBW <=DW_BX M xHB>@:XDMRLCU:\XDL[M"!9>OCKG \XpB<[M_G LJ L<[M >OLBS[M.BXDLNCu:S[C7i=DGMRGt} e M+Uq\S<PHM S{=?EK<S[CKG \HWRM4<PHM4L[C!ZW_BX?XDMRGuG JKE B>@=?W4:PTBL[CS{>OCKGM 1X P=DWNPn=DL\HLNMRGnBL^BTBL=DL UqCSnL<N%B =?X?=?<$J BEHG PTBS>OCE=DWmBETBX?J L=DLw=?E < 4CICU1<PHM|B::dM EHGMRG :TB:dM S[L_}lQPHM`G JETB>@=DW :PTBL[CS(>OCKGM X^=DL B .HC\HS=DM"S.L[M S=DMRL(M"x :TBEHL=DCE CUg<PHMuLJ L<[M > L<NB<[MnC7i M SB`>OC7iK=?E]m<=?>OM =?EHGC .}gZ<PTBL1:S[C7iMRGh<[*C dM.BElM VW =DM EK<<[CKCXtUqCS1M"x :XDCS=?E]V<PHML<[S\HW <\S[M.CU{:dM S=DCKG =DW BEHGcW JW X?=DW.LJ L<[M >OL_} CS[MRC7i M S 4MV]=?i M|, B S=DM"UGMRL[W S=?:<[=?CE CU1<PHMVPTBS>OCE=DW|<SNBEHL UvM S Uq\EHW <=DCE ' '*$. ( BEHG@WRC>@>OM EK< CEOL[C>OML=?>@=?XpBS=?<=DMRL dM 3< 4MRM EV<PHM'*$.FBEHGu<PHM1G JKETB>@=DW:PTBL[CS+>OCKGM X9} QPHM';$. ]M EHM SNBX?=?A_MRL1<PHMWRCEHWRM :<1CU{<SNBEHL UvM"SQU \ETW"<[=?CEc<[CnX?=?EHM_BS<=?>OM(:dM S=DCKG =DW ' )5( LJ L<[M >OLBEHGm=DL1<PK\HLBElM VW =DM EK<<[CKCXtUqCSPTBS[>OCE=DWwBETBX?JL=DL7} .{=?ETBX?X?J 4M(:HS[C7iK=DGM BuL\>@>VBSJmCU^<PHM.B::dM EHGMRGc:TB:dM S[L;BEHGmX?=DL[<Q<PTM(:6\ X?=DW_B<=DCEHL \:dC, E P=DWNPc<PTM.B::dM EHGMRGc:TB:dM S[L*BS[M TBLNMRGt}. . .
(290)
(291) ) \XDL[MO>OCKG \XpB<=DCE ? ! PTBLdMRM E B::X?=DMRG =?E B =DGMOSNBE]MVCU1B::X?=DW_B<=DCEHL_}mE M_BSX?J M"xB>@:HX?Mh=DLu<PHMmC7i M E <[M >@:dM SNB<\S[MlWRCEK<S[CX1LJ L<[M > GMRL[W S=-dMRG J(C\J ? 1=?E _%5} ;<PHM S M"xB>@:XDMRL PHM S[MnUvMRMRG1TBWNaIPTBL dMRM E = >@:HX?M >OM EK<NM G \HL=?E]h:\XDL[Mu>OCKG \XpB<=DCE =?E ! W X?\HGM`SNBGHBSuL[JL<[M >OL"~ 8#Zb M XDMRW <S[CX?JK<=DW|>OM <NBX4S[M" HE=?E]F:XpBEK<[L$ ? 75%1BEHG L =?<[WNPHMRG >OCKGM :dC 4M S1WRCEKi M S<[M S[L& ~#
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(293)
(294) !#"$% & #!' )(* +!,- #. σ(t). .{=?]\S[MO $E:\<L=?]ETBX. σ(t). s(t). ./. BEHGcC\<:\<:\XDL[M*Uq\EHW <=DCE. s(t). CU Bu:\XDL[M(>OCKG \HXDB<NCS_}. >OCKG \XpB<=DCEO<PHMQXDM E]<P t −t CU <PHMLNB>@:X?=?E]=?EK<[M SiBX ' W_BX?XDMRGu<PTMQLNB>@:X?=?E].:dM S=DCKG ( =DL(WRCEHL<NBEK< P=?XDMwUvCS*C<PHk+1 M S(<$J:dkMRL(CUg>OCKG \XpB<=DCE =?<(=DL;iBS=pB%XDM@BEHGFBVU \EHW <=DCE CUg<[PHM =?E:\<L=?]ETBX σ(t) } s(t). τk. ak. tk. .{=?]\S[M`# wMRW <NBE]\XpBSw:\XDLNM@=?E. G \SNB<=DCE. τk. t0k + τk. t0k. < PHMVLNB>@:X?=?E]I=?EK<[M SiBX BEHGhXDM_BG =?E]`MRG ]M B<<=?>OM t0 }. tk+1. [tk , tk+1 ]. =?<P. B>@:X?=?<\HGM. ak. k. $E <PH=?L@LNMRW <=DCE 4M`UvCKW \HL@CE PTB<@=DLn:S[ C T%B X?J <PHM|>OCL<@WRC>@>OCE <$JK:dMmCU;:H\XDL[M >OCKG \XpB<=DCEY}*e MwWRCEHL=DGM S*>OCKG \XpB<[CS[L P=DWNPF:S[CKG \HWRMw:\XDL[M Uq\EHW <=DCEHL*<PTB<(BSNMwWRC>u! :dCL[MRGFCU S[MRW <NBE]\XpBS:H\XDL[MRL_}.TCS(L[\HWNP :\XDL[Mn>OCKG \XpB<[CS[L_bY<PHMuC\<:\<(:\HX?LNM Uq\EHW <=DCE W_B, E dM 1S=?<<[M ElM"x :X?=DW =?<X?JmCEc<PHM(UqCS> s(t) =. PHM S[M. (. ak , t ∈ [t0k , t0k + τk ) 0, t ∈ [tk , t0k ) ∪ [t0k + τk , tk+1 ). D= L4<PHM*:\XDLNM !$B>@:HX =?<\TGM.BEHG PHM S[M t b t0 BEHG τ BS[M;EHCE !9EHM ] B<=?i M(S[M_BX EK\>u! dM S[L`LNB<=DLU J=?E] tk ≤ t0 ≤ t0 + τk < tk+1 } k QPHkMl:TBSNBk>OM <[M S τk =DLV<PHMc:\XDL[M"!& =DG <P BEHG t0 GM <[M S>@=?EHMRL <PHM@k:dCL=?<=DkCE CUQ<PHM@XDM_BG =?E]IMRG ]MOCUQ<PHM@:\XDL[M}`MRM!.{=?]H} #|UqCSwBE =?X?X?\HL<SNkB<=DCEY} C>OM@CUg<PHMn:TBSNB>OM <[M S[L>OM EK<=DCEHMRG %B dC7i Mw>VB_J dMuWRCEHL<NBEK< P=?XDMuC<[PHM S(>VB_J dM BnU \EHW <=DCEICU^<PHM=?E:\<L[=?]ETBX σ(t) }+ 4CVWRC>@>OCE W_BL[MRL ? ^BS[M=?X?X?\HL<SNB<[MRGc=?E .{=?]H}Ty dM XDC .}+QPTM"JcBS[M }1) \XDL[M"!$B>@:X?=?<\HGHM.>OCKG \XpB<=DCE ' )d*) ( ZEh:\XDL[M"!$B>@:X?=?<\HGM.>OCKG \XpB<=DCEl<PHML B>@:X?=?E]@=?E<[M SiBXDLBSNMCU^M \TBXYX?M E]<[PlBEHG PHM S[M T > 0 =DL`<PHM LNB>@:X?=?E] :dM S=DCKGt},$<VPHCXDGL t0 = t L[C <PTB< t = kT ak. & !. k. s. s. k. k. b.
(295) y. <PHMhXDM_BG =?E] MRG ]MlCU(<PHMc:\XDL[MlWRC= ETW"=DGMRL/ =?<P <PHM,dM ]=?EE=?E] CU(<PHMlLNB>@:X?=?E] =?EK<[M SiBXQBEHG τ = τ > 0 ∀k L[Ch<PTB<uBX?Xg:\XDL[MRL PTB_i MO<PHMVLNB>OMVG \SNB<=DCEY}cQPHM :\XDL[M"!$B>@:X?=?<\HGkMRL a BS[M(iBS=pB%XDM BEHGlBS[M.GM <[M S>@=?EHMRG,J`<PHM.L=?]ETBX σ(t) } k. # }1) \XDL[M"!& =DG <Pl>OCKG \XpB<=DCE ' ) e )( ZEV:\XDLNM"!& =DG <P|>OCKG \XpB<=DCE|<PHM;L B>@:X?= EH]w=?EK<[M SiBXDLQBS[M;CUYM K\TBX XDM E]<PmBEHG t = PHM S[M Ts > 0 =DL1<PHM LNB>@:X?=?E]V:dM S=DCKGt}QZ<1PHCXDGL t0 = tk L[C@<PTB<<PHM.XDM_BG k=?E] kTs MRG ]M|CU<PHM`:\XDL[M|WRC=?EHW =DGMRL =?<P <PHM/dM ]=?EE=?E] CU<kPHM|L B>@:X?=?E] =?EK<[M SiBXBEHG LNC;<PTB<+BX X :\XDL[MRL^PTB_i M <PHMQLNB>OMB>@:X?= <[\HGM}^QPHM4:\XDL[M"!ZG \S B<=DCEHL ak = a > 0 ∀k B [ S M i B S p = B % D X M BEHGlBS[M.GM <[M S>@=?EHMRG KJ`<PHM.L=?]ETBX σ(t) } τ k. . 0. Ts. 2Ts. 3Ts. . y 4C@<$J:dMRL1CU{:\XDLNM(>OCKG \XpB<=DCE
(296) =?<PcL \TBS[M(:H\XDL[MRL :\XDL[M"!$B>@:X?=?<\HGM >OCKG! \XpB<=DCE ' )d;(BEHGh:\XDL[M"!& =DG <Pl>OCKG \XpB<=DCE ' ) e ("}. .{=?]\S[M.
(297) . 0. Ts. 2Ts. 3Ts. "!$#&% ')(* " )%,+. QPHM4<PHMRL=DL^=DL{:S=?>VBS=?X?J UvC W \HLNMRGnCEu:\XDL[M"!& =DG <P@>OCKG \XpB<[MRG ' ) e )(LJ L <[M >OL_bBX?<PHC\]P :TB:dM S13 WRCEHL=DGM S[L>OCS[M*]M EHM SNBXt<$J:dMRLQCU>OCKG \XpB<=DCEYbH= ETW"X?\HG= EH]O)d* } $E|<PHM(L:dMRW =pBX W_BL[M.CU^) e b <PHM:\XDL[M(U \EHW <=DCEl=DL$ S=?<<[M E s(t) =. (. a, t ∈ [kTs , (k + dk )Ts ) 0, t ∈ [(k + dk )Ts , (k + 1)Ts ). PHM S[M a > 0 =DL4<PHM(B>@:X?=?<\HGM.CU <PHM*:\XDL[MRLBEHG d ∈ [0, 1] =DL4<PHM*LNC!ZW_BX XDMRGhG \<$J`W JW XDM P=DWNPlGM <[M S>@=?EHMRL<PHM.G \SNB<=DCEICU^<PHM k-/. :\XDL[M} $E ) e bY<PHM`:\XDL[M"!& =DG <P =DL iBS=pB%XDM|BETG =?< =DLnGM <[M S>@=?EHMRG KJ <PHMV=?E:\<nL[=?]ETBX } QP H m M q U \ H E W < D = C T E B X [ S M XpB<=DCEHLP=?:d M <3 4MRM E σ(t) BEHG <PHMcG \<$J W JW XDMRL d >VB_J <NBa M σ(t) >VBEKJmG = stM S[M EK<UvCS>OL_} $ElBETBXDC]J =?<P ? !Zb64 M.G =DL<=?E]\=DLPc<PHM(UvCX?XDC =?E]O<3 4COW_BL[MRL_} k. k.
(298)
(299) !#"$% & #!' )(* +!,- . }1) \XDL[M"!& =DG <Pl>OCKG \ XpB<=DCE CU{<[PHM HS[L[<a=?EHG ' ) e c !N ( ZE )+efl!N b;<PHM G \<$J W"J W XDM d =DLcGM <[M S>@=?EHMRG KJfLNB>@:X?=?E] <PHMF=?E:\<cL[=?]ETBX k BWRWRCS[G =?E]V<[C. PHM S[M. dk = F (σ(kTs )). ' (. dk = F (σ(kTs + dk Ts )). '# (. =DLnBcEHCEHGMRW S[M_BL=?E] Uq\EHW <=DCE GM" HEHMRG CE R LNB<=DL UqJ=?E] 0 ≤ F (σ) ≤ UqJK=?E] F (0) = 0 ("} # }1) \XDL[M"!& =DG <Pl>OCKG \XpB<=DCE CU{<[PHMLNMRW CETGma=?EHG ' ) efl!$# ( ZEc) e l!$#n<PTMG \<$JmW J W XDM d =DL<PHM.L[CX?\<=DCEc<[CVBEcM K\TB<=DCElCU^<PHM(UqCS>. '. F (·) BEHGh<$JK:=DW_BX?X?JhLNB<=DL 1, ∀σ ∈ R. k. PHM S[M. L B<=DL TMRL<PHM.LNB>OM BL[L\>@:<=DCEHL;BL=?El) e c!N } ;::X?=DW_B<=DCEHLwCUQ) e BS[MnUqS[M K\HM EK<=?E <PHM TM XDG CUQ:dC 4M S M XDMRW <S[CE=DWRL_}V2^xHB>@:XDMRL =?EHW X?\HGM L =?<[WNPHMRGf>OCKGMFWRCEKi M S<[M S[LcBEHGf=?EKi M S<[M S[L_b;L[MRM MRW <=DCE }~ydM XDC .} $E L\HWNP GM i=?WRMRL7b <PHM.) e =DL1CUq<[M Eh=?>@:XDM >OM EK<[MRG BWRWRCS[G =?E]V<[C. PHM S[M4L B< 4CS[GL_bH) e. F (·). dk =. L B<. 'y (. [0,1] (σ(kTs )). =DL<PHM4LNB<\HSNB<=DCE dM <3 4MRM EuA_M S[C(BEHGnCEHM}{$EnC<PHM S 0), 1) !N := c =DL\Hmin(max(·, LNM G =?<P F (·) N L B< (·) } = [0,1] ;EHC<PHM SQ<[MRWNPE=K\HM;UvCS4=?>@:XDM >OM EK<=?E]V ) e =?E|:dC 4M S1M XDMRW <S[CE=DWRL=DL4<[Cw\HLNM(BwWRC>u! :TBSNB<[CS SNB>@:VUq\EHW <=DCE|BLg=?X?X?\HL<SNB<[MRG`=?/ E .{=?]H}H}^'*M S[Mb <PHM1=?E:\<4L=?]ETBX L B< (σ(t)) =DL WRC>@:TBS[MRG|<[Cw<PHM*L B Q!9<[CKC<P|SNB>@:|U \EHW <=DCE r(t) = 1 (t >OCKG T ) }^< <PH2 M d[0,1] M ]=?EE=?E]OCU s M_BWNPhLNB>@:X?=?E]u=?EK<[M SiBX <PHM*:\XDL[M;U \EHW <=DCE s(t) <NBa MRTL4iBX?\HM a BEHG|=?<4S[M >VB=?EHLWRCEHL[<NBEK< \EK<=?X4<[PHM|L=?]ETBX σ(t) =?EK<[M S[L[MRW <[Lu<PHM`SNB>@:Y} Q<n<P=DLn<=?>OM`=?EHL<NBEK<u<PHM`:\XDL[MVUq\EHW <=DCE <NBa MRLQiBX?\HM(A_M S[CVBEHGh=?<S[M >VB=?EHL1A_M S[C@\EK<=?XY<PHM dM ]=?EE=?E]`CU{<PHMEHM"x <1LNB>@:X?=?E]O=?EK<[M S ! iBX PHM S[Mu<PHMu:S[CKWRMRL[L=DL(S[M :dM_B<[MRGt}uQPHM k- . L =?<[WNP=?E]h=?EHL<NBEK<=DLGM <[M S>@=?EHMRG KJl<[PHM L>VBX?XDMRL<1EK\ > dM S d ∈ [0, 1] P=DWNPlL B<=DL TMRL<PHMEHCEX?=?EHM_BS;M K\TB<=DCE [0,1] (·). s. k. dk =. L B<. [0,1] (σ(kTs. ' (. + dk Ts )) .. $EcC<PHM S 4CS[GL_b<P=DL=DL;BuW_BL[M.CU^) e l!$# } $Eh<PHM ) e c!$#u<[MRWNPE=K\HM GMRL[W S=-dMRGIB%dC7i M 4M.CEX?JcBX?XDC 4MRGhUvCS1CEHM.:\XDL[M=?ElM_BWNP LNB>@:X?=?E] =?EK<[M SiBXv} $E :dC 4M SVM XDMRW <S[CE=DWRLO<P=DL@S[MRL<S=DW <=DCE =DLOCU <[M E =?>@:dCL[MRG <[C B_i C=DG L[C!ZW_BX?XDMRGFLX?=DG =?E]hL[CX?\<=DCEHL 5 PHM S[Mn<PHM S[M@BS[MnL[M i M SNBX^L =?<[WNP=?E]m=?EHL[<NBEK<[L =?<P=?E CEHM LNB>@:X?=?E]m=?EK<[M SiBXv} KX?=DG =?E]hL[CX?\<=DCEHLBS[MuBL[LNCKW =pB<[MR
(300) G =?<P EHCEHX =?EHM_BS:PHM EHC>OM ETBmL\HWNP B$L = Uq\S[W_B<=DCEHL;BEHGcWNPTBCL7bLNMRM 5bN {BEHGhS[M"UvM S[M EHWRMRL1<PHM S[M =?EY} $Eh<PHM.WRCEK<[M"x<CU^:dC 4M SM XDMRW <S[CE=DWRL_bH<[PHM) e l!N (<[MRWNPE= K\HM ' y (4CstM S[LBG iBEK<NB]MRL L\HWNP B* L dM =?E] XDMRL[LOL[M EHL=?<=?i Mm<[CFEHC=DL[McBEHG B]=?E] CU(WRC>@:dCEHM EK<[L 8 Z} ) e c!N lBXDL[C >VBa MRL*=?<M_BL[=?M S<[C|>OCKGM X <PHMuLJ L<[M > G JETB>@=DWRL(=?E B|G =DL[W S[M <[Mu<=?>OMwUqSNB>OM 4CS
(301) a P=DWNP W_B/ E dM\HL[M"Uq\XHUqC5S dC<P|WRCEK<S[CXtBEHG|BETBX?JL[=DL_}^';C 4M i M S_b) efl!N =?EK<S[CKG \HWRMRLBGG =?<=DCETBX GM XpB_JmWRC>@:TBS[MRGc<[CO) e c!$# }. %. . #.
(302) 8. r(t). 1. σ(t). 0. 2Ts. Ts. 3Ts. a. .{=?]\S[M H 4C>@:TBSNB<[CSSNB>@:Uq\EHW <=DCE BEHG=?E:\<WRCEK<S[CXKL=?]ETBX σ(t) }QPHM+G \SNB<=DCE CU{<[PHM(:\XDLNMRL=DL1GM <[M S>@=?EHMRG K J`<PHM=?EK<[r(t) M S[L[MRW <=DCEICU r(t) BEHG σ(t) } 0.
(303) . . % + . 2Ts. Ts. 3Ts. # . QPHMnEHCEX?=?EHM_BS.BEHGFG =DL[WRCEK<=?EK\HC\HL.WNPTBSNBW <[M S=DL<=DWRL.CU4BV:\XDLNM"!& =DG <PF>OCKG \XpB<[CS>VBa MRL WRCEK<S[CX BEHG BETBX?J L=DL.CUQ) e LJ L<[M >OLWRC>@:X?=DW_B<[MRGt}OQP=DLPTBL>OC<=?iB<[MRG B|EK\>dM S CU B::S[C_x =?>VB<[M>OCKGM XDLUqCS<PHMG JETB>@=DWRL1CU^) e L[JL<[M >OL7}^$Em<PHML[MRW <=DCE,dM XDC 4M S[M i=?M LNC>OMCU^<PHMRL[M>OCKGM X?=?E]|B::S[CBWNPHMRL_} WRC>@>OCE <[MRWNPE= K\HM UqCS(B::S[C_x =?>VB<=?E]m:\XDL[M"!9>OCKG \XpB<[MRGFLJ L<[M >OL=DL;S[M"UqM SS[MRGI<[C BL1B_i M SNB]=?E]H}+'*M S[Mb<PHM(:\XDL[M(>OCKG \XpB<[CS1=DLQS[M :XpBWRMRG KJ|BnWRCE<=?EK\HC\HLQUq\EHW <=DCEcCU<[PHM =?E:\<^L[=?]ETBX σ(t) }^;EHM4WRC>@>OCEOB_i M SNB]=?E]B::S[CBWNPu=DL{<[CS[M :XpBWRM4<PHM :\XDL[M >OCKG \XpB<[CS =?<PI<PHMwWRCSS[MRL:dCETG =?E]mL<NB<=DWwWNPTBSNBW <[M S=DL<=DW ? Z}.TCS*BO:\XDL[M"&! =DG <P >OCKG \XpB<[CS_bd<[PHM L<NB<=DWnWNPTBSNBW <[M S=DL<=DWn=DL;<PHMw<=?>OM"!$B_i M"S B]MniBX?\HMnCU+<PHMw:\XDL[M.Uq\EHW <=DCE PHM E <PHMw=?E:\< L=?]ETBX σ(t) =DL1WRCEHL[<NBEK<_}+$EcC<PHM S 4CS[GL_b<PHM.L<NB<=DW.WNPTBSNBW <[M S=DL<=DW =DL1G"M HEHMRGlBL. $ !. L<NB< (σ. 0 ) :=. 1 Ts. Z. Ts. s(τ )dτ. PHM S[M s(t) =DL<PHMu:\XDL[MnUq\EHW <=DCE WRCSS[MRL:dCEHG =?E]l<[Cm<PTMu=?E:\< .TCS<PHM.W_BL[M.CU^) e l!N BEHGh)+efl!$#u=?<=DL1M_BLJ|<[C@LNMRM(<PTB< 0. σ(t) = σ0 =. WRCEHL[<NBEK<7}. L <NB< (σ ) = aF (σ ). 0 0 QPK\HL_b6=?E.<PHM+) e LJ L<[M > CEHM 4C\XDG.S[M :XpBWRM+<PHM :\XDLNM^U \EHW <=DCE s(t) =?<P.<PHM^Uq\EHW <=DCE } aF (σ(t)) QPHMuB_iM SNB]=?E]hB::S[CBWNP =DL;:TBS<=DW \XpBSX?JlWRC>@>OCE 1PHM EI>OCKGM X?=?E]mL =?<[WNPHMRGI>OCKGM / g!Z/ W CEiM S<[M S[L_} ZE <P=DLWRCEK<[M"x<_bYBE B_i M SNB]=?E]m>OM <PHCKGCXDC]J S[M"UvM SS[MRG <[CmBLL<NB<[M L:TBWRMcB_iM SNB]=?E] QBL@C\<X?=?EHMRG KJ l=DGG XDM S[CKC a
(304) ~# Z} =?]CS[C\HLu>VB<PHM >VB<=DW_BX <S[M_B<>OM EK<[L 4M S[M`:S[C7iK=DGMRG =?E ~# b ## Z}I2 x<[M EHL=DCEHLn<[CIS[MRL[CETBEK<uWRCEKi M S<[M S[LnPTB_i M|BXDL[C dMRM Ec>VBGMbHLNMRM ~y# b$y Z}. . #. .
(305)
(306) !#"$% & #!' )(* +!,- . QPHMOL<NB<NM@L:TBWRMVB_i M SNB]MRG >OCKGM X+=DL.CUq<[M E L=?>@:XDMVBEHG =DL<PHM S[M"UqCS[MVCU <[M E \HL[MRGFUqCS RW CEK<S[CXgGMRL=?]EY}n';C 4M i M S_bt<PHM@L<NB<[MuL[:TBWRM@B_i M SNB]MRGF>OCKGM XgGCKMRL(EHC< BWRWRC\EK<UqCS(<[PHM S=DWNP iBS=DM <$J CUEHCEX?=?EHM_BSu:PHM EHC>OM ETB <PTB<uW_BE C WRW \Su=?E L =?<[WNPHMRG >OCKGM|WRCEKi M S<[M S[L_} QP=DL QBL1EHC<[MRGc=?E ? _% PHM S[M.<PHM B\<PHCS[L;LPHC <[PTB<L[C>OM.CU <PHM BL[L\>@:<[=?CETL1>VBGM =?Ec<PHM.B_i M SNB]=?E]O<[PHMRCSJhBS[M.MRL[L[M EK<=pBXtUvCS<PHMiBX?=DG =?<$JmCU^<PHM B_iM SNB]MRGc>OCKGM X9} $< PTBLBXDL[ C dMRM E|EHC<[MRGtbL[MRM ? _# YBEHG|S[M"UqM S[M EHWRMRLQ<PHM S[M =?EYb<PTB<Q<PHM*L<NB<[M*L:TBWRM(B_i M S ! B]MRGn>OCKGM X EHMRMRGuEHC<^W_B:<\S[MQ<PHMQL<N%B =?X?=?<$J :S[C:dM S<=DMRL+CU <PHMQLJL[<[M >c} .TCS{=?EHL<NBETW Mb<[PHM B_i M SNB]MRG.>OCKGM XW_B E dMgL<N%B XDM M iM E <PHC\]Pn<PHM BW <\TBXLJ L<[M > =DL EHC<_} .H\S<PHM S>OCS[Mb<[PHM B_i M SNB]MRG >OCKGM X EHMRMRG EHC<(]=?i M@BE BWRW \SNB<[M@GMRL[W S=?:<=DCE CU PTBS>OCE=DWu:S[C:dM S<[=?MRL L\HWNP BLQG =DL<\S TBEHWRM*:S[C: B] B<=DCEY}gQP=DL QBLG =DL[W \HL[LNMRG`=?E ~y
(307) Z} .{=?ETBX?X?J 4M*EHC<[M*<PTB<GMRL=?]E L:dMRW = TW_B<=DCEHL.<$J:=DW_BX?X?JI=?EHW X?\HG* M dC\EHGL.CE <PHM@L<NB<[M7C\<:\<_}uQPHM@L[<NB<[MuL:TBWRMOB_i M S ! B]MRGV>OCKGM X GCKMRLgEHC< S[M :S[MRL[M EK<4<PHM;L<NB<[M7C\<:\<4S=?::XD2 M P=DWNP`=DLg=?EPHM S[M EK<4=?E|L =?<[WNPHMRG WRCEKi M S<[M S[L;BEHGh:dM_Ba|iBX \TM L;BS[M<PHM S[M"UqCS[M.\EHGM S[MRL<=?>VB<[MRGt} ;MRWRM EK<X?J <PHM S[M PTBL dMRM E B EK\ > dM SlCUn:TB:dM S[L ~y bRHb7 b _# b6#5b7y
(308) b7y b7y b_
(309) 70 # Zb BGG S[MRL[L=?E]*<PHM+=DLNL\HMRLCUHL<N%B =?X?=?<$J bPTBS>OCE=DWQBETBX?JL[=DL{BEHG S=?::XDM MRL<=?>VB<=DCEuCUTL =?<[WNPHMRG >OCKGM+:dC 4M S{WRCEKiM S<[M S[L7}QPHM UvCKW \HL CU<PHMRL[M :TB:dM S[L{G = s M S_b \< <PHM JL[PTBS[M <PHM+i=DM <PTB< W XpBL[L=DW_BXL<NB<[MmL:TBWRMmB_i M SNB]=?E]F=DLn=?EHL\ VW =DM EK<VBEHG <PHM J GM iM XDC: >OCS[MmL[C:P=DL[<=DW_B<[MRG >OCKGM XDL_} .TCSBn>OCS[M BWRW \SNB<[M LJ L<[M >jGMRL[W S=?:<=DCEYbTL[C>OM B\<PHCS[L1PTB_iM(>OCKGM XDMRGl) ef LJ L ! <[M >OLn=?E G =DL[W S[M <[M`<=?>OM} QP=DL@BX?XDC 1LwUqCSn<PHM`L 1= <NWNPHMRG ETB<\S[M|CU<PHMV:XpBEK<n<[
(310) C dMmBW"! WRC\EK<[MRGVUvCS4M"x:X?=DW =?<X?J`BEHG`<PHMS[MRL[\X?<=?E]uG =DL[W S[M <[M;<=?>OM>OCKGM Xd]=?i MRLQBE|M"xBW <4S[M :S[MRL[M E ! <NB<=DCE CU<PHMVLJ L<[M > L<NB<[M`B< <PHMVLNB>@:HX =?E]I=?EHL[<NBEHWRMRL_}mQPHM`G =DL[W S[M <[MV<=?>OM`B::S[CBWNP QBL\HLNMRG|UvCS1L<N%B =?X?=?<$JhBETBX?J L=DL1= E Hb9 # {BEHGh=?Ec:TB:dM S CU{<P=DL1<PHMRL=DL_} /*=DL[W S[M <[Mw<=?>OMw>OCKGM XDL*PTB_i MnBXDL[C|L[M Si MRGIL\HWRWRMRL[L Uq\X?X?JlBL(! B TBL[=DLUqCS;PKJ S=DG WRCEK<S[CX GMRL=?]E`<[MRWNPE= K\HMRL4L\HWNPmBLgPKJ S=DGO>OCKGM Xd:S[MRG =DW <=?i M;WRCEK<S[CXtBEHGVS[M XpB6x MRG`G JETB>@=DW:S[C! ]SNB>@>@=?E]Hb+L[MRM pb ~# b b_ _8 b #y b[ Z}c$E :TB:dM Su/ CU1<P=DLw<PHMRL=D L 4M`WRCEHL=DGM SuWRCEK<S[CX LJEK<PHMRL=DL TBLNMRGmCEcBnLNB>@:XDMRGhGHB<NBw>OCKGM X P=DWNPcGMRL[W S-= dMRL<PHM(M i CX?\<=DCEcCU<PHML<NB<[M B<O<PHMhL B>@:X?=?E] =?EHL<NBEHWRMRL_5b \<`BXDL[C :S[C7i=DGMRLVBFS[M :S[MRL[M EK<NB<=DCEfCU*<PHMh=?EK<[M S !ZLNB>@:XDM dM PTB_i=DCS_} C>OM;S[MRWRM EK< 4CSaVCE|)+ef LJ L<[M >OLgS[M X?JVCE`<PHM;LNC!ZW_BX XDMRGmG JKETB>@=DW;:PTBL[CS4>OCKGM X P=DWN*P QBL{=?EK<S[CKG \HWRMR*G K4J gM S]PHMRL[M
(311) ~y Z}{QPTMQG JKETB>@=DWQ:PTBL[CS^>OCKGM X=DL^ C <NB=?EHMRG U SNC> ! B .TC\S=DM S;LNM S=DMRL;M"x:TBEHL=DCE CU <PHMwLJL[<[M > L<NB<[M C7i M S*B@>OC7i=?E]V<=?>O4 M =?EHGC .}1Z< W_BE dM|L[MRM E BL@Bc]M EHM SNBX?=?A7B<=DCE CU<PHM|L<NB<[M|L:TBWRMmB_iM SNB]MRG >OCKGM X P=DWNP =?EHW X?\HGMRL P=?]PHM SPTBS>OCE=DWRL ' <PTBE@z \HL<1<PHM.WRCEHL<NBEK< ("}4Ec=?EK<S[CKG \HW <=DCEI<[C@<PHM G JKETB>@=DW.:PTBL[CS >OCKGM XY=DL]=?i M Ec=?EIMRW <=DCE # dM XDC .} QPHMG JETB>@=DW(:PTBL[CS>OCKGM XtPTB#L dMRM ElB::HX =DMRGh<[C@BnEK\ > dM S1CU^G = s M S[M EK<:HS[ C XDM >OL_} .TCShM"xB>@:XDMb;=?<mPTBL dMRM E \HL[MRGf<[C GM iM XDC: M VW =DM EK<cL=?>w\XpB<=DCE <[CKCXDLmUqCShL =?<[WNPHMRG LJ L<[M >OL ? _
(312) b # BEHGUvCS L<N%B =?X?=?<$J BETBX?JL[=?LCU / g!Z / WRCEKi M S<[M S[L_}{QPHM : B:dM"SNL ? _# b
(313) b H \HL[M+<PHM G JETB>@=DWg:PTBL[CS>OCKGM X UqCSL[<N%B =?X?=?<$J BETBX?JL[=DLCUTBE\ > dM S{CUHG = stM S[M EK<{WRCEKi M S<[M S <[C:dCXDC]=DMRL_}lQPTM LNMV:TB:dM S[L UqCKW \HLnCE C:dM E XDCKC: LJ L<[M >OL_b \<w<PHM`W XDCL[MRG XDCKC: W_BLNMO=DL BXDL[COW C>@>OM E<[MRGt} QPHMl<PHMRCS[M <=DW_BXBL:dMRW <[L`CU<PHMlG JETB>@=DWc:PTBLNCSV>OCKGM 2 X 4M S[MIBGG SNM LNL[MRG =?E ~y Z} $E <[P=DL(:TB:dM S_bB`EK\ > dM S CU4WNPTBX?XDM E]=?E]IWRCEKiM S]M EHWRM@=DL[L\HMRL QBL=DGM EK<= TMRG BEHG L[C>OM \HL[M"Uq\X BETBX?J L=DL<[MRWNPE= K\HMRL 4M S[M.C\<X?=?EHMRGt}. #.
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(315) 5. QPHMuG JETB>@=DWn:PTBL[CS(>OCKGM X :S[C7iK=DGMRL(=?E UvCS>VB<=DCE B%dC\<(<PHMnPTBS>OCE=DWRL.CU4B|G J ! ETB>@=DWFLJ L<[M > <PS[C\]P <=?>OMIiBSJ=?E] .TC\S=DM ShW CKM VW =DM EK<[L7} E BX?<[M SETB<=?i M <[CKCX*UqCS WNPTBSNBW <[M S=?AR=?E]n<PHMPTBS>OCE=DWRL =DL <PHM1PTBS>OCE=DW1<S BEHL UqM S+U \EHW <=DCE ' '*$. ( ~#% b y8 bp y bpK5 $} QPHM.'*$. =DL;BEc=?1E HE=?<[M G =?>OM"ETL=DCETBX =?E:\< !ZC\<:\<;>VB: P=DWNPc]M EHM SNBX?=?A_MRL;<PHMEHC<=DCE CU <SNBEHL UqM S Uq\EHW <=DCEO<[CX?=?EHM_BS+<=?>OM1:dM S=DCKG =DW ' )5( LJ L<[M >OL_}{Z<+=DL <PK\HL BEOM VW =DM EK<g<[CKCX UqCSGMRL[W S-= =?E]O<PHMPTBS>OCE=DW WRC\:X?=?E]L1=?Eh<=?>OM:dM S=DCKG =DW LJ L<[M >OL_} Eh=?EK<S[CKG \HW <=DCEI<[C <PHM.';$. =DL]=?i M Ec=?EIMRW <=DCE y dM XDC .} QPHM.';$. PTB$ L dMRM ElB::HX =DMRGc<[C@L =?<[WNPHMRGh>OCKGM:dC 4M S1WRCEKi M S<[M S[L1<[C dM <<[M S1\EHGM S ! L<NBEHG <PTM"=?SnPTBS>OCE=DW|:S[C:dM S<=DMRL_} MRM pb ~y
(316) 1P=DWNP L[PHC 1Lw<PTB<w=?<w=DLnMRL[L[M EK<=pBX4<[C \EHGM S[L<NBEHGc<PHMPTBS>OCE=DW WRC\:X?=?E]L=?Eh:dC 4M S;WRCEKiM S<[M S[L7} 3QMRW_B\HL[M4<PHM4';$.l=DL=?1E HE=?<[MQG =?>OM EHL=DCETBX9b<PHM S[MQBS[MQL[C>OM =DL[L\HMRL{CE 4M X?X !9:dCL[MRG EHMRLNL_} 4CEKi M S]M EHWRMQ=DL[L\HMRL^S[M ] BS[G =?E]<PHMQ'*$. 4M S[MW XDM_BS[MRGu=?E ~yHbpy8 Z}^M XpB<[MRG 4CSawCE@1) LJ L<[M >OL1W_BElBXDLNC dM(UqC\EHGh=?E y bZK5b9 Z} $El<P=DL;<PHMRL=DL_bT<PHMnG JKETB>@=DWRL;:HPTBL[CS;>OCKGM X^L[M SiMRL*BL(* B BL=DL1UvCS*BETBX?J L=DL=?
(317) E dC<P :TB:dM S;3 BEHG *}H)^B:dM S f=DLGM iC<[MRGc<[COPTBS>OCE=DWnBETBX?JL=DLCU+) e LJ L<[M >OL_}g$Ec<P=DL :TB:dM S 4MnWRCEHL=DGM S.BVL \TBS[Mw<S\EHW_B<[MRG B::S[C_x =?>VB<=DCE CUg<PHMw:PTBL[CS(G JETB>@=DWRL_}*QPHM <S\EHW_B<[MRG LJ L<[M > =DL*\HL[MRGI<[CmGM S=?iM@BOUqS[M \HM EHW JIGC>VB=?EF=?E:\H< !ZC\<:\<>VB) : P=DWNPF=DL BETBXDC]C\HLn<NCl<PHM`'*$. CU;BE ),LJ L<[M > BEHG P=DWNP S[MRG \HWRMRLn<[CFBc<S\EHW_B<[MRG ';$. UqCSQC:dM E|XDC C:mL[JL<[M >OL7}{$E`:TB:dM SQ3 4M;WRCEHL=DGM SQL[<N%B =?X?=?<$J`BETBX?JL[=DL4CUY:\XDL[M"!9>OCKG \XpB<[M_G LJ L<[M >OL_}e M=?EK<S[CKG \HWRM*B.LaM <S\HEHW_B<[MRG|B::S[C_x=?>VB<=DCEmCU <[PHM:P BL[CS G JKETB>@=DWRL4BEHG \HL[Mw=?<(<[C|WRC>@:\<[Mu<=?>OMn:dM S=DCKG =DW \TBG SNB<=DW@tJ B:H\EHC7icUq\EHW <=DCEHL_}e MuBXDL[CmLPHC PHC <PHMX?=?EHM_BS=?A_MRG`LaM <S\EHW_B<[MRGVG JETB>@=DWRLgW_BE dM\HL[MRG@<[C<[C.GM S=?iMB*UqS[M \HM EHW J@GC>VB=?E =?E:\< !ZC\<:\<(>VB:FBETBXDC]C\HL*<[CO<PHMwCEHM >OM EK<=DCEHMRGF%B dC7i M}1)^BS<*CU+<PHMwWRCEK<S-= \<=DCE CU1<PHMO<PHMRL[=DL =DL <[CILPHC BcWRCEEHMRW <=DCE dM 3< 4MRM E <PHM`G JETB>@=DWV:PTBL[CSw>OCKGM XBEHG <[PHM '*$.4}. . . .
(318) . . $!4. 36. * . . %. #. #. #. ( # )
(319) ?35. 46 A3. ;. )0BC;. ). F, 3F 3F. vp vp s. vs. vs 0. .=?]\SNM. 8 =?]PK< L<[M : !ZGHC El/g!Z/ WRCEKiM S<[M S_}gYM"Uq< :\XDL[MRGhiCX?<NB]M}. #. QPHM HS[L<(M"xHB>@:XDM 4MnWRCEHL=DGM S(=DL*<PHMnL[<[M : !ZGC E /g!Z/ WRCEKi M S<[M S ~#
(320) GM :=DW <[MRG =?E).{=?]H} 8 }(QPHMw:\S:dCL[MuCUg<PHMnL<[M : !ZGC E WRCEKi M S<[M S*=DL*<[C|WRCEKi M S<*<PHMnL[C\S[WRMniCX?<NB]M =?EK<[ClBh / i CX?<NB]M v B< L[C>OM@]=?i M E S[M"UvM S[M EHWRMOXDM iM X9}`QPHMOL[C\S[WRM v =DL WRCEKi M S<[MRG vs KJ C:dM E=?E] BEHG W XDCL[=?E] o <PHMmL =?<[WNP s B<@BlP=?]P U S[M K\HM EHW J} QPHMmL =?<[WNsP :S[CKG \HWRMRLOB.
(321)
(322) !#"$% & #!' )(* +!,- . i CX?<NB]M v =?El<PHM.LPTB:dM CU+BuS[MRW <NBE]\XpBS2 QB_i M}gQPHMwB_i M"S B]MiBX?\HM.CU^<P=DL QB7iM(UvCS> =D#L HX?<[M S[MRGcp C\<1\HL=?E]`BnXDC :TBL[L1 HX?<[M S;BEHGm<P=DL1]=?iMRLBEIB::S[C_x =?>VB6<NM./ i CX?<NB]M} QPHMXDM i M X CU^<PHM. / C\<:\<i CX?<NB]M.GM :dM EHGL;CEc<PHM G \SNB<=DCEICU^<PHM:\XDLNMRL1CU v }gZE p C<PHM S 4CS[GL7b <PHMXDM i M Xt=DL1WRCEK<S[CX?XDMRG KJ`:\XDLNM"&! =DG <Pl>OC G\XpB<=DCEY} $!4. 3 7. 0, '3. #
(323) 3. ,3535 vac. s1. + v − s3. s1,4. ac. vdc. s2,4. vdc 0. s2. .{=?]\S[M . s4. s2,3 −vdc. +1=?]PK< iCX?<NB]M"!ZLNC\S[WRM.=?EKiM S<[M S_}gYM"U < :\XDL[MRGhi CX?<NB]M. #. QPHMOL[MRWRCEHG M"xHB>@:XDM 4M@WRCEHL=DGM S.=DL<PHMuiCX?<NB]MOL[C\S[WRMu=?EKi M S<[M S ~#
(324) gGHM":H=?W <[MRG =?E .{=?]H} }(QPHMw:\S:dCL[MuCUg<P=DL(GM iK=DWRMn=DL;<[C|WRCEKi M S<BV]=?i M EF/ L[C\S[WRMwi CX?<NB]Mw=?EK<[ChBE B::S[C_x =?>VB<[MO i CX?<NB]M}wQPHM@2 QB_iMnUqCS> =DLB::HS[C_x=?>VB<[MRGKJ L K\TBS[Mn:\XDL[MRL.BL =?X?X?\HL<SNB<[MRGc=?, E .{=?]H} } C :S[CKG \HWRM;<PHMS[MRW <NBE]\HXDB#S QB_i M1UqCS> <PHM;L =?<[WNPHMRLBS[M;C:dM SNB<[MRGmBUqCX?XDC 1L_} 9U s b B S[MwW XDCL[MRG BEHG s b s C:dM EI<PHM S[M =DL*B@:dCL=?<=?i M.i CX?<NB]MwC7iM S;<PHM.XDCBGt}19U s b s BS[1M s4 C:dM EhBEHG s b s W XDCL[2MRGV3<[PHM S[M=DLQB.EHM ] B<=?iM;i CX?<NB]M;C7i M S <PHMXDCBGt} .{=?ETBX?X?Jb= U s1 b s4 BS[M 2 4 W XDCL[MRGlBEHG 2s b 3s C:dM Ec<PHM S[M.=DLA_M S[C@iCX?<NB]M C7iM S1<PHM(XDCBGt} 1. . 3.
(325)
(326)
(327) . . QPHM.:TB:dM S[L3 BEHG f=?Ec<PHM.<PHMRL=DLWRCEHL=DGM S*BETBX?J L=DL TBL[MRGcCEl<PHM.L[C!ZW_BX?XDMRGlG JETB>@=DW :PTBL[CS|>OCKGM X9} QP=DLmL[MRW <=DCEf]=?iMRLmBE =?EK<S[CKG \TW"<[=?CE <[C <PHM G JKETB>@=DWI:PTBL[CS|>OCKGM X BEHGVGMRL[W S-= dMRLg3< 4CwB::S[C_x=?>VB<=DCE|<[MRWNPE= \HMRL \HL[MRGOCEV<PHM1= E6 HE=?<[MG =?>OM EHL=DCETBX :PTBL[CS G JETB>@=DWRL_} C;C\S aEHC XDMRG ]Mb<PHMgG JETB>@=DWg:PTBL[CS>OCKGM X QBL=?EK<S[CKG \HWRMRGw=?E <PHM TM XDGwCU:dC 4M S M XDMRW <S[CE=DWRL(BL*Bu<[CKCX UqCS>OCKGM X?=?E]`<PHM.<SNBEHL[=?M E<[L;CU+L =?<[WNPHMRGIWRCEKiM S<[M S[L7bTLNMRM pb ~ b #8 b yy b y Z} .H\S<PHM S>OCS[Mbt=?<;PTBL dMRM E B::X?=DMRG =?EI<PTMnBETBX?J L=DL*CUg:dC 4M SLJL[<[M >OL ? b % BEHG`UvCSQGM iM XDC:=?E]OM VW =DM EK<1L=?>w\XpB<=DCEh<[CKCXDL4UvCSQL =?<[WNPHMRGmWRCEKi M S<[M S[L_bL[MRM ? _
(328) bZ# BEHG S[M"UqM S[M EHWRMRLO<PHM S[M =?EY} Z<@PTBLVBXDL[) C dMRM E \HL[MRG UqCSOL<N%B =?X?=?<$J BETBX?J L=DLOCU(L =?<[WNPHMRG :dC 4M S WRCEKi M S<[M S[L_bHL[MR M pb ? _# b9
(329) b9H Z} QPHM|G JETB>@=DW`:PTBL[CSn>OCKGM X4=DLu
(330) B .HC\S=DM S@L[M S=DMRLwS[M :S[MRL[M EK<NB<=DCE CU1<PHM|L<NB<[M`CU*B LJ L<[M > C7i M"SwBm>OC7iK=?E]c<=?>O! M =?EHGC .}VQPHM@:S=?EHW =?:XDMO=DL.=?X X?\HL[<SNB<[MRG =?E .{=?]H}5}O$E <P=DL H]\S[M 4Mw=?>VB]=?EHMw<P B< x(t) =DL(BVL[CX?\<=DCE <[C|L[C>OMnG JKETB>@=DWnL[JL<[M >c};,<=?>OM =?EHGC =DL;:XpBWRMRGFC7i M S;<PHMw<=?>OM@B6x=DL*L[<S[M <[WNP=?E]`UqS[C> <PHMnW \SS[M EK<(<=?>OM t TBWNac<[C`<=?>OM t − T PHM S[M T > 0 }O34JI=?EK<[M ]SNB<=?E] C7iM S.<PH*M =?EHGC QM@WRC>@:\<[M .TC\S=DM S WRCKM VW =DM EK<[LnCsU. . . s. #
(331) !. . . . .
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