B.S. DHILLON and ZHIJIAN LI

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1 Ieol Joul of efobly Egeeg, Vol., No., Ocobe 5, pp RAMS Coul ed Id B.S. DHILLON d ZHIJIAN LI Depe of Mechcl Egeeg Uvey of Ow Ow, Oo, N 6N5 Cd Receved o Ocobe 3, 4 Abc: Th ppe pee hecl odel o pefo vlbly ly of obo-fey ye hvg -edud obo d -edud bul- fey u wh coo-cue flue. The ye flue e d he plly fled ye ep e e ued co, d he fled ye ep e ued bly dbued. The uppleey vble ehod ued o develop geelzed expeo fo Lplce fo of e pobble d ye vlble. ey Wod: ece, obo, ye, fey, vlbly, coo-cue flue. Ioduco I ece ye, obo e cegly ued vou eco of duy fo pupoe uch c o po weldg, udewe exploo, oue pce exploo, fe fghg, edcl d, d elevg hu fo pefog hzdou. Accodg o he Ieol Fedeo of Roboc IFR he woldwde dul obo populo eched 35, 987 Sole, 987, d ceed o 7, 9 97 Ued No, 998. A coevve foec fo dul obo fo 5 965, Ued No,. Robo fey of uo poce Rez 985 poed ou, I ho, fey coce becue geelly obo e exeely og, f, def, dub, bld, uoc, d heefoe dgeou. Ove he ye ube of eou ccde d ohe fey-eled poble volvg obo hve occued Ncole, 987; Ngch, 988; Dhllo, 99. Thee boluely o doub h obo h o be fe d elble. A uelble obo y led o ufe codo, hgh ece co, coveece, ec. Theefoe, o pefo obo elbly ly, he couplg bewee elbly d fey u be cefully codeed. Moeove, obo elbly d vlbly lye, he occuece of coo-cue flue ovelooed d oly geel flue e codeed. A coo-cue flue y be defed y ce whee ulple u o elee fl due o gle cue Dhllo, 983; Dhllo, 999. Ude uch codo, he ed eul y o pee ue pcue egdg he cul ye elbly d vlbly. To pove ye elbly, he cocep of edudcy wdely eployed, d c lo be ppled o obo-fey ye. Coepodg uho el: dhllo@gee.uow.c 79

2 8 B.S. Dhllo d Zh L Theefoe, h ppe pee vlbly lye of obo-fey ye hvg - edud obo d -edud bul- fey u wh coo-cue flue. The bloc dg of h obo-fey ye how Fgue d coepodg e pce dg gve Fgue. The uel d lee d he boxe d ellpe of Fgue deoe ye e. A B C A: -decl obo B: -decl fey u C: coo-cue flue Fgue : The Bloc Dg of he Robo-Sfey Sye wh Coo-Cue Flue A e =, ll -edud obo d -edud fey u opeg. The obo-fey ye c fl due o he flue of ll obo o he occuece of coo-cue flue. Noehele, he obo-fey ye wll fuco olly ul le oe fey u d oe obo e opeg olly. The ye goe hough [+] dc opeg e. A coo-cue flue c occu oly f le wo u cludg le oe obo e fucog uccefully. Oce ll fey u fl, he obo y coue o opee ul he flue of he h obo. The degded o fully fled obo-fey ye y be eped. The followg upo e oced wh h odel:. The obo-fey ye copoed of decl obo d -decl fey u.. The edud obo d fey u e opeg uleouly.. All flue e clly depede. v. All flue e d he plly fled ye ep e e co. v. The ep of he fey u h he poy ove he ep of he obo whe he ovell ye he plly fled opeg e. The fled obofey ye ep e c be co o o-co. v. A eped obo o fey u good ew. v. The ovell ye fl oly whe ll he cve obo fl.

3 Sochc Aly of Sye Cog N-Redud Robo 8. Noo The followg ybol e oced wh he odel: h e of he ovell obo-fey ye: fo = e ll obo d fey u e pefec wog codo; fo =+q whee =,,,, d q=,,, - e -q obo d - fey u opeg olly whle q obo d fey u hve fled; fo = + -

4 8 B.S. Dhllo d Zh L e oly oe obo opeg olly whle - obo d ll fey u hve fled. h e of he fled obo-fey ye: fo =+ e obo d fey u hve fled; fo =++ whee =,,, e obo fled whle fey u e fucog; fo =++ e he obo-fey ye fled due o coo-cue flue. e Co flue e of fey u. Co flue e of obo. c Co coo-cue flue e of he obo-fey ye e ; fo =,,,, +-. Co ep e of he fey u e =+q; fo =,,, d q=,,, -. Co ep e of he obo e ; fo =,,,-. x Fe ep e evl. x Te-depede ep e whe he fled obo-fey ye e d h elped ep e of x; fo =+, ++,, ++. p x,x The pobbly h e, he fled obo-fey ye e d he elped ep e le he evl [x,x+x]; fo =+, ++,, ++. pdf obbly dey fuco. z x pdf of ep e whe he fled obo-fey ye e d h elped e of x; fo =+, ++,, ++. obbly h he obo-fey ye e e ; fo =,,, +-. obbly h he obo-fey ye e e ; fo =+, ++,, ++. Lplce fo vble. Lplce fo of he pobbly h he obo-fey ye e ; fo =,,, +-. Lplce fo of he pobbly h he obo-fey ye e ; fo =+, ++,, ++. AV Lplce fo of he obo-fey ye vlbly whe he obofey ye wog wh le oe fey u. AV Lplce fo of he obo-fey ye vlbly whe he obofey ye wog wh o whou he fey u. AV Robo-fey ye e-depede vlbly whe he obo-fey ye wog wh le oe fey u. AV Robo-fey ye e-depede vlbly whe he obo-fey ye wog wh o whou he fey u. 3. Aly Ug he uppleey ehod Gve, 963; Gg, 963, he ye of Equo oced wh he Fgue odel c be expeed follow: d x x dx d,

5 Sochc Aly of Sye Cog N-Redud Robo 83 d d,,..., fo fo d d 3 d d 4,,..., fo ] [ d d 5,,...,,...,, fo d d 6,,..., fo fo d d 7 ] [ d d 8,...,, fo d d 9 fo whee c,,..., fo c fo c,,..., fo c c ] [

6 84 B.S. Dhllo d Zh L fo,,...,,,..., fo,,..., c c [ ] c fo fo,,..., fo x, x, x x, x fo,,..., The oced boudy codo e follow: ], [ fo,,...,, c A e =, =, d ll ohe l e pobble e equl o zeo. Ufouely, vey dffcul o ob geel foul fo obo-fey ye elbly d vlbly ug Equo -. Howeve, fo pecl vlue of d, Equo - c be olved. Seg = fo =,,,- Fgue, whch e obo e epble he opeble e of he obo-fey ye, geelzed expeo e developed. Thu, Equo -3 becoe: d x x dx d, 3 d d 4 fo,,..., d d fo 5 whee c fo,,..., c c fo

7 Sochc Aly of Sye Cog N-Redud Robo 85 Equo 4- e e. 4. Se obble d Sye Avlbly.e., =, fo =... - Ug Lplce Tfo echque d he l codo Equo 4 5, we ge x, x dx 6 7 fo,,..., fo 8 9 fo,,..., [ ],,..., fo,,..., fo,,..., fo [ ] 3 fo,,..., 4 x, x, x x, x 5 fo,,..., d he boudy codo: ], [ 6, c fo,,..., 7 Solvg dffeel Equo 5, we ge he followg expeo:

8 86 B.S. Dhllo d Zh L Sce, x x x,, e exp[ d ] 8 fo,,..., x, dx fo,,..., 9 d ogehe wh Equo 8, we ge Z, 3 fo,,..., whee Z x x, e exp[ d ] dx 3 fo,,..., o x Z e z x dx 3 z x exp[ fo,,..., x d ] x whee z x he fled obo-fey ye ep e pobbly dey fuco. Le =+q fo =,,,, d q=,,, - d deoe he h e of he obo-fey ye, whee d q e he ube of fled fey u d fled obo, epecvely. Splfyg Equo 7 8,, d 3 4, we ge q whee g U h f h gq [ q [ f gh fo ] g g l [ l g gq [ ] gh q l h[ q ] lh,,,..., q, q,,3,..., q [ fo q,,..., q 33

9 Sochc Aly of Sye Cog N-Redud Robo 87 U [ fo q,,..., U [ [ q q U q U q [ [ fo fo,,..., q,,...,,,..., q,,..., q [ fo q,,..., U q [ Slly, plfyg Equo 9 d, we ob q whee q q fo fo fo,,..., q,,..., Fo Equo 33 d 34, he Lplce fo of he h e pobbly c be expeed,,,..., fo q, 35 q,,,..., whee he fuco of he Lplce fo vble,. q q q fo q,,..., q g gq g [ l g [ q ] l 37 g gq U [ f [ ] gh q l h f h gh h[ q ] lh,,,..., fo q, q,,3,...,

10 B.S. Dhllo d Zh L 88 The Lplce fo of he pobble of ll he ye e dd up o /,.e., 38 Solvg Equo 33-38, we ge H Z ] [ 39,,,...,,,,...,, q q fo H 4 H Z ] [ 4,...,, fo whee ] [,...,, fo c c Z H Thu, he Lplce fo of he obo-fey ye vlbly wh le oe wog fey u H AV 4 Slly, he Lplce fo of he obo-fey ye vlbly wh o whou wog fey u gve by H AV 43 Subug he Lplce fo of z x fo dffee ep e dbuo o Equo 4 d 43, d g he vee Lplce fo of he eulg equo, we c ge he e-depede ye vlble, AV d AV.

11 Sochc Aly of Sye Cog N-Redud Robo 89 Refeece []. Dhllo, B S. 983, Relbly Egeeg Sye Deg d Opeo, V Nod Rehold, New o. []. Dhllo, B S. 99, Robo Relbly d Sfey, Spge-Velg, New o. [3]. Dhllo, B S. 999, Deg Relbly: Fudel d Applco, CRC e, Boc Ro, Flod. [4]. Gve, D.. 963, Te o Flue d Avlbly of lleled Sye wh Rep, IEEE Tco o Relbly, Vol., pp.3-8. [5]. Gg, R.C. 963, Depedbly of Coplex Sye Hvg Two Type of Copoe, IEEE Tco o Relbly, Vol., pp.-5. [6]. Ngch, M. 988, Te Fl Accde due o Robo Jp, wow, H.R. d e, M.R.Ed, Egooc of Hybd Auoed Sye I, Eleve, Aed, pp [7]. Ncole,. 987, Sfey oble Reled o Robo, Roboc, Vol. 3, pp.5-. [8]. Rez, C.A. 985, Sfey of Robo, Nof, S.. Ed., Hdboo of Idul Robo, Wley, New o, N, pp [9]. Sole, E. 987, Socl d Ecooc Fco of Roboc Sye, oceedg of he 987 Mly Roboc Aoco, Vco, B.C., Cd, pp []. Ued No Ecooc Coo fo Euope 998, Wold Roboc 998- Sc, Me Aly, Foec, Ce Sude d ofbly of Robo Ivee, Ued No, New o. []. Ued No Ecooc Coo fo Euope, Wold Roboc - Sc, Me Aly, Foec, Ce Sude d ofbly of Robo Ivee, Ued No, New o.

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