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MFIoAblAl.tAJlt,43AlilCl4[{TE3APA3HoTEMnoBbIXCI4CTEMynPABnEHyIR

xl, k+l : 11, P* t'x2, t* tuil

xz,k+r =xt, o*T 4-tukt

Ao rcl , k, xz, k, up - c]Ke.lrfrpbll xi, 0 , 12, 0 - (tuxcl'tpo-

IAI{bI.

Cucreua (14) nPltuer BI{.q

Pt, k: Pt, ** r + e(* P?,n., * 2P2,& + I -F

* Pt, *+ t * 1) + O(c2);

Pz, k: Pr, **, + iPr,ft + I + \'r, o* r*

*r(Pl,k* r * Pl,&* {Pz, t*, * lPs, tn t) -- Pz, *+ i) * O(o2);

P3, k: I", u+ 1 -l- 1 +

* u(P1, /rn 1 * P2, kn 1) + O(e2)'

Facuten"rstouee npeo6pa3oBaHI'Ie

Pt, k: v1, * 4t.(q, t * ZZ, k) + OG\;

Pz,k:ZZ,t*2Pt;t. t-_,(q*.ry) + oGz);

f ) * ot"r

NPI,TBOAHT EE K BI,IIIY

uk: uk* 1-r {3u21r*t * 4uk+ r + 1) l- O(J);

vAK 681.s

; -Zz.tot -Zj,k*L _"(,,,, r', zz,o: tT , -T- o\vrrt[zz,t+tr

I - W) +322, k+t*2z3,knr) + o(u2);r'2)tr,

i 23, k:9# + Ezz,k+ I + o(ez),

I .o" nepBoe )rpaBHeHlle He3aBHclIMo' Ha'{anulble yc-

I ;;;;;;, zi,'N, zt,7r,r np,HrMalor cxelylou{yrc SopW:

1,, : -t!.- + aG\, zz, N: - 1 + f ' + o('2),

I .r* *1 - S, + o(e2).,, ,3,.1/- J 9''I

, Cmrcor x$Teparylbl

I l. Barlrct J. P', Monaco S', Nomand-Cyrot D" Pantalos N' Dis-I cretization Schenres i"?iiilil;-sr'-',.,l*iv Perturbed Systems //' ;j;;

"f iir" lbG leEe cbc isst' Briehlo-n P' 443-448'

r '^"2'. N;;;-n- S. ii;s;i;.-i;'ituutio"n Methodo-logv il control

s rti. *t' 71" j fE f b ;;f;it"ein"t ti ne S e ries' 34' Petcr Peregrirtus

i lta., tgaa.: "'"31 "futio,

n. S', Price D' B', flibey^'I' L' Sineular Perturbations

I u,,iri,*'i-.;;. (s;;riiil Dil;i;'control Sistems - a-n over-

, view // Proc. or tt" iilirt^c;Irf' ;; fiition and Contr'' L,os An-

, ncler.'b A. 1987. P.2096-2103I t"'"4.' iilo".,;'c. r.,-l"lr*"s"n fi' f', Maue'qora A' II' PaaHo-

r Mepl{a, no ManoMy nop.*.tpy vcrofiuo-911 x cra6urxsauwt LLtc-

r Koerr{htx .rnrynrprrd rorlayucnuux AI'rHaMIl\lecxw cnoeu f fi fiil;;;;;,ii61I"""* iets r I c'.2r-2e'i ^::"n*rp;;;t ri. n., co6oner B. A. KoHcrprylPll:'i.X:l"jI paculenaexns ueluueirgux c[HrynqpHo Bo3MVIueHHbIx AI'{QQe-I oerruuzLnr,s ** "n"rf,i"iJ- ArOO"ir.rirI{MLHLIe ypanrrexr'ra' 1 995, r :i. T. 4. c. 569'-s78.'

- . 6. Boponaena [I. 8., Co6oaen B' A' Aerorunogur(u'l M]loluTeM-

' ,iouu,* cltcrcM- CauaPa: CMC, 2000'| "- i fleoso3laficxnia a" a, KypcTeop,{n ar]roMaTuqecKoro yIIpaB-

| ,,.n*. M.: I{aYra' 1986'

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u(e / e -R; xi e R'' ; Aij -- MaTplllrbl ooorBercrBylolqllx

pa3Mepuoc'reii, npnveu Aii: Ay(t,t1, "', en), i,i : ffi ',{r}Jrfl }orcJt uItuIKI4Mlr !{ orpaHr{qeHHbIM}I MaTpuqHbIM[

OyHrcuu.qraH, t1, i: T, n, - MaJIbte IIoJIo)g{TerbHbIe

IIaPaMeTPbI, 66: 1.

Cucr:euu c oAHHM MaJIrIM napaMerpou 6rrnn pac-

cMorpeltbl n pa6oTe [il. Eyaeu npeAflonararb' qro

Marpuqilble rDyHxr{eIN-..4 ii, (AnnG,0, "', 0))-1 o6la'ua-

IOT,rlocTaTorIHl,IM TIIICJIOM I{enpepbIBHbIX H OrpaHI4-

LIEHi{bIX TIACT}IbTX IIPOH3BOAI'IbIX IIO BCEM APryMEHTAM

npu / e R, sy . (0, ul ] u co6ctueHHble 3HaLIeHIlt'I

1,,: l.i(/), i: T,fn MarpI'IuH Anr(t,0' "'' 0) yAonrte*

'rBoprtlor HepaBeHcrBy Rel'; < -2P < 0'

Ha nePnou uare cAeJIaeM 3aMeI{Y

P3, k: zt, r, i \ + ,(+r,, o *

M. M, CenaeHosa,

carvrapcran rocyAapcTBeHHafi SKOHOMnqecKaf

aKa!,eMfifl

,Q,er<o m no3vl t&m ffi 0 ffi cre MCI HecKorIhK&tMr4 tspeMeHF[blM&4

Pacqeruumruee upeo6pa3osflHfie' Paccuarpunae'r-

cs rl,IneliHafi cxcreMa

infieki:i= irtr*,, i:0;i,

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' Mac[.rxraoannpa

Ileaaeaemclnemoidexoltnosutluutluaertuotxcu\eyflflpllosogttyu4elilwx cucme*l, ocuoe attuuil Ha meopuu wt mezpalutbtx

iiiiiiop* i, 6wcmpwx - u ue\ne n nux deutrce uui' rcomop wfi

n o38 o tx e m cg e c m u ucxo r) uy to c u c m eW K' 6tt o'l tt o - 0 ua e o H art b'

,',rii;uiay. fiauuuu *t*oa ucnolt$yemc' npu ucctedoeauuu

sadiaqu ycnroivuoocmu lilepeemu4ecrcoil cucmeuu'

6u Mexa'rpoulrKa, aBToMarEBaIu'r, yupaBfielrue I'lit 8' 2004

cennemosa [vI- M- o AeKoH,tnogr4tlt4fl a4creM c HecKonbKilMl,,t BpeMeHHun,lr uacura6aur

rltt--l*i: ,i -, n t1,H)$, E1t ...t rn)y|,,k=i*1

i= [n_-l;-. - .,I -,- "-lxn: ln 1- 2 t) $, t1, ..., En)xi,

i=0.ITo6sI rlortytIH]'], c],IcTeM y

i .t rr-lf1 'rii : ZAliyj ,i:a,n*t;

k-0 j=0tlrlr

fi trj,l: Alnyl,k=l

.1 1 rf[e A;j : Ai* AirLj , i, j: 0,n-l; A)n : Arr-n-l il .

I 1 t1,Lj Ai^j=0k-j+l

Marpu.nrue cpyr-rxquu t), Ul, i,j : 0, n- l, uo-ryr 6urr riattrgeusl ts BHJIe acuMnrorlrr{ecKrjx pa3Jlo-)KCH}III

,) : rlorlt,'o (/, el, ..., t,t* l)iffj :

oln ,1, *)'n (,, u,,..., cr, _. r).

KoaSOHqHer{.tbi o'rltx pa3roxeHufi onpe4elaior.cnoAHO3HaqHo I,r3 COOrBercrByIoruHx ypanuenurl

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x (Au + a1,l,,l): a,

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pprrrHbre tlyr.rrquu a),, U),_ r,n_ r (r, 0, ..0))-"r o6.,ra-

IaIOT /IOC"IATO{HLIM qLICJtoM HenpepbuJi{r,tx }r oipat{t.r-qeHHbtx qaclHbtx npoH3BOAHbtX r10 BceM apfyMeH.t,ilM

nplt / € ,t; er: e (0, oj ], + - r; pr co6cuier.u{bre 3naqe-

I{HJr }.i: i,i(/), i: \ n;.1, Malp}il$,t A,r" ,.r_ 1(/, 0,..., 0) ygorurrrruopJrror r{cpaDei{crny:

Rel";( -2s.K0, Ie fi.B noc.neguett cilsreMe cfler?leM 3aMeHy rrepeMeHHbix

r a n-l .vi : yi + fl ,o lti {r, t1, ..., rn)!2,,_t,

k= i+1

i: 6, n:1;

v),-r = y?;-t a 'z' 4(/, er, ..., ,,,)+.

t=0

B peey.nrrare nonJ,n{r,rM crrcreMy:i 1 n-2ll tt,ii: Z Aiiyj , i:

k=0 j=0o, n-2;

n-l .) ) 1

1I c*Y]*t : Al,,.l,a-l Yi-r;k=l

r I ,t, i), : ,q),n ,), ,

k=l1 t n*2 n_l

rrc Al,-t,z_t :,tr)_r,n_t - I n uot? e),r_r;

A?i: Ali +-e],,-r 4, Li:=#.'Mar-puvHue gyuruur- N , 4 , ,, j: [IT7, uo-

ryr 6rt'rl uaftregu B Br,rre acuMnrorr.rqecKux pa3Jlo-xeuufi

12=Iok'2'k'''i - *?otr- t Lj -- (/, €1, ..., tn - z, en)i

4 : olorf, -, 4'o (,, ,r, ..., En - 2, En).

Koe$OraqlreHrbr 3rHx pa3roxeH[fi oA.HosHa.{uootrpellenrrcTcr{ H3 COOTBeTCTnyrcqnx yparuetrufi

,) ,l t n-lAn.-t,j '* An.t,r-t L; -'"tl'Ekt -

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l=0 k=l+l

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- rt a?,_ r,z_ r : o, i, i: 6fr-1,11 T.

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j'6'' : al|o' yl,-' * a6;' ,i-' ,' q j,l"t : n'i;' ,'d-' -r Air' ,'i-' ,

.n- | ,rr*1 n_lt.lt2),2 . : 422 ll ;

.2 ) )r: t...r.'rr _ ly;-t : Ar.. l,r_ j yn_t;

t i:..u,, j'ln : A),n ll,,

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Ma'rpfi.rrmre rlyrirqnu L;-' , j:0,1, r,,roxHo l,rc-

Karb B ilr{re acuMrrroraqecKr{x par.noxeuurt Ljt - I :

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MexarpounKa, anToMarp.[g&r1urr, yirpamJxerrue Nb B, 2604 "1,

MFTOAbI AHMt43A K1 CI4HTE3A PA3HOTEIUNOBbIX CI4CTEM YIIF'ABJIEHHq

- nfo tf 4-I'k 1t, ,1, e3, ...,er,) ,s coorBe'rcrryrc- ; rrs cloruercrilnou,x ypauueHufi

ulux vpauueuufi i Ai;, n- air, L _ orl * r1l(Alir, * ,,tlpt ty: o;:tt-l ., ! IqqLi-r +srurLld-tU3;'* n'i;2 t,t,-t).t i a,i;r +er (At;, + A;;tt,,tt.-.rtk _r{afr:s.

+ "^ rn-1'xzLt ui;' + Ai;, t'j-I ) : ] *..r,*Ao'affrre yc.noiivunocrx{ o,eprelfi.rec*ofi csc-,n-2: A';;"1 A;;2 on-', ./:0, I i biT::J:ffiJflfI#:fT:ffi::ffiffiT:fiffi.#

Marpnvuue ovuruuu H:; ' ,i : 0, r, Moxi:io Hc- i id8: XIfi;J::rffiifJrlT*"fffr*H#ffiffi.;Karb B ,Hre ac,Mrlro'r,yecxr.rx pa3"rroxeH, ii r{, 't - I ;L::frJ#ff';-?:ffi'HHX"#T;?:#;ffi;:

olo "lrr'i-t'k(t, e1, 4, ..., tn), r.rs ypan.ueuuri i P53:Il##fl':##lf:.ffiTflTfffir#Jril:,,1,2 fi-' n 4' ni;' : t1t2A!r, q-, * 1 l;';1.'Sl#;X:fi';";.,1*ffi;##- 6vaerr,

*,:l^i,,Hi ,+ Aiz-,,,:0,r I ",jrffixT;;H:f.ir;umffi'ffi:#ffiI"ol-1il tt-M utale npeAnoJlafaeM, r.ITO MZlTpI,IqItLIe I

oyu*uur.r Ai;' ,u';; t (t,0, ...,0))-r oorrn;r;;, l, T,* : -rr,Tal'oqnbrM qHcJroM HeripeprirHbix r.r orpal{r4areH-Hbrx qa_ i _. rls,cfHblx npol't3BoAHblx no BceM apryl!(eHraa.{ npu I e n;

" 7',J,; : -c1Ao.1 + AtaQt- (lr * 2)Sr _

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-2p<0.'a r,o* ,, 'JrT : Liac2 * Ktsz"1- B21L6pi

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y'i-' = tl + r1t, t1t .,.t ur)yt-r i 'off : au * aq1'

IrorIylIHM "6novno-glraroxarbltylo" cficrcMy l, ,r,+: ut - ),1Au1 *.r1 i

.'.n * ,fi n .n ,,ls = A's6r[, qii : A'it yi: i T rtl..2,trzi!i-, : ,qi;, ,i-r, ,, .,

t'r-li : *LrAa2 - szi

n-l ) ^ ', ,.dLQ1

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.rc Ai,: A,i.'*t1r,tl,,'4: sn-t _u1rg_1;1 or.ix1:r,l1ii'i#l,"Ib##1;"?,ur"#,;#1;f;qlo = A[it * ,q[r't. i craHuHH pelyntlrop'Irciorut uz:0),

I .rt, iD - orrutorteHule cKorbxeHr,Irl nepBoro !I rlro_Marpuvlllte @vurqgg I, .Fruoxrro lrcKaTb B Dnqe i poao'a.rr.puropuB, coorBercr,eHHo;c,Mnrorl{qecK,Ix pas'uoxexNri r aLr -- orKrloHeltue or}Iolre]I Htr pacxot\aBo/fbr B Ha-I = '

.1, rk,, I nopuol;r u'ro.rlbt{e n pr"roov og ilonHoli Harpy3K-Ut * tlolt L U, e2, ..., En); r Typ6H[ri,r npu to : l.i,g, H: If6 (r"- Sr;or"r.;** V._Lt * \_ k ,,h, | ,rorax cKopocrb, ,6 _ cI,IHxpoHHafl yrrroaafl cKo-t- e1Il,.(1, EZ, ..., En) r pocrb, 11 _ Hanop rflnpaBr[qecxofl ryp6prnu; ,;.16 _&>0 r \', "1, "', ent

1 uanop ts ycralrol]uBlrreMc.fl pextue);

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Cemexoaa M. M. o .Eexouno3ruuc cHcreM c HecKonbKrMh BpeMeHHblMu Maclura6ar"tlt

a"- or-ororiloourenlrrr $arrrrvecxoro npe- | uocrn craHqrft; pl, pz6yleu cqr'ITarb col{3Mep}rMbr-

BbrrrreHlu ypoBrur Bo,qbr B pe3epByape Ha.q )ipoBHeM I *r, 6nusronna x ].noAoxpaswiuuaKcrllolpoHHoMy;. r 7

Aai, i : 1,.2, - orKIIoHeHlre rrIpaB,fl{qecKoro or- I ga*t*rtttt Ty, Trr, Trr, Tp, T, Trr, Trr, To -Kpbrrwr l-fi ryp6rrrt (r. e. oruonerlle orHorueHllrl

!

pacxoAa i-ft ryp6rarrr ,,p]r AaHHo* rroro*"r;;* | nocroxnnbleBpeMe,rl', ar{Me,r{o' Tv- flocrosHHzls

npaBJUIIouux JIorIaroK, cl{HxpoHHoft ymonofi cKopo- i :!:y"* BroprqHoro perynrpoBaHH'fi' KorAa qacrory

"rr r ru'ope H: r/e B roM y"r"rorrr-"r;;F i ;ffi;l*1:r*r::ilff,11ffi::J:il#;Tffi;

ue, roroprtft.(oJn(eu Hacryrn{Tb rIocJIQ sar}rrraHllrl }Ic- I oonarurs): Z. . i : l. Z, _[ocroJrH,ax npeueHu f-rocJleflyeMoro [epexo,{Horo [poqecca, K pacxoff (2!g i ' ni'

nomroft Harpy3Kr{ ryp6unu [p]r 0) : o0,, H: H1); i cepso,(Bnrarelu; 7p - nouoflI{Ha.fl, paB}dafr rlep]IoAy

Lql - orKJro6eglre orHocr{TeJrbnoro pacxoAa [ep- | role6anux ypoBufi BoAbI B ypaBHI{TenbHoM pe3epBya-

noft ryp6unrr; I pe, AeJIeHI{oMy na 2n; 2n' - nocro''IHHa'I BpeMeHII

A6tz - orKlroHeHlre orHocrmeJrbHoro yrna Mex[y I rslpaBrrrlecKoro y\apauepnoft craHqr[; Trr, TJ, -ocfrirlrporopon rrepBoft u ntopofi MaIIITIH; I [ocros,Hbre r{Hepqr* y rrepBoro r4 BToporo reHepa-

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rlrBHbrx ryp6rn rapaMerp B: r. EJrn;;;" ", ?':

r'r2' Tp: tnrpt T": m2r'"' T": m,r"'

"'*'t-^"-^*' i Tr: mzr* Tg: m2rg, ga ry, ,f,., ,rr, rD, rsrt r3r,1

ryp6uri4 - eto BeJII{,ILIHa nops.qKa ), a msscex 6es i k;r";r'"t#f##rffi#ffi::ffiffi H_ucKrrroqerfifl ryp6rn flapaMerp ,4 ouyruuo ,6olblue I nofi Aecsrofi.c. flapaudrprr K1, -K2 Bcerfla rroJro]o'ITeJrbl{bl I BneAeu o6osHaqeHl{, 6: m2L6n, D2: rr,rt +

flapauerp B - rocrarorlno MaJIoe qIrcJIo, ,, Br.,

g : 2#, rse hg- rrorepn Harlopa n rpy6onponose. i *

-fi"rrt''

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rrapauerp y: A, z* - 3naqeHlre qpeBbrrrreuwl i . ,dur :_ | , Brzrrr-.

ypoBrurBoAbrB]gggpErgpe,aAypoBH"ruoaorp*- | "' di : -i'uz+ ffi'sz;

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urnl yror; 5rz - orHocrnrenbnnft yror Mex.try ocrIMH ', *z rrr# - u1- iru,

* 'r#rs2 - r,1Acr1i

poropoB nepnoft u nropoft MaruI'IH; o, : : Jt-=- . IYt 51 +S2' t " dL,a"

i: l,--Z,rae 9i; E:iloilHbre HollilHaJrbubre Molri- ', fl"" df - -s2- x2La2'

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M ETOAbI AHMl,l3A tl Ch HTEsA PASHOTEM nOBbIx chcTEM ynPAB'jlEHt4tl

t dLqt _ | -2Br v2 * Blh,x *o1-rr-71- - trr

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^'",0*:*,u, (#*,.t)*I,Icnormsyx MeroA AeKoMrlo3lrqlil(, uuroxeimrrfi

Bbrrue, lrccneAyeM ycrofiwmocrr cucrerrlrr (1)'

flycrs Ha rIepBoM Ilrare BbrrloJrlrflrorcf, ycnoBlrg

1+ PBr > o: l"r 2 oi )'z 7 oirr ' Tsr

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3. Cenenora M. M. YnpasJuleMocrb xenugefinux MgororeM-noBLD( cltcreM // Tes. wwt. VII Mexrynaporxoro ceuxxapa "Yc-rofi.ruBocrb u xoae6axng norxxeftnrrx c[creM ynpaanenx.a'. Mo-crsa, I4ITY PlGl,22*24 uas.2002 r. C. 115-176.

- C2ffio 25 cenmadpt 2004 e. I noc. Kaqueeau, Kptm, Vrcpauaacocmoumcfl

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