Stability analysis of sampled-data fuzzy-model-based control systems

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erol Jorl of Fzzy Sye ol. o. Je 8 9 Sbly ly of le- fzzy-oel-be corol ye H.K. L E.W.S. C brc er ree e bly ly of e le- fzzy-oel-be corol ye. o vege e ye bly -S fzzy oel eloye o reree e oler ye. le- fzzy coroller eloye o cloe e feebck loo. De o e lg cvy of e le- fzzy coroller coy roce c colce e bly ly. Coeqely e eg ly roc for coo-e ye co be le. Frerore e erfecly ce gre of eber le o e fvorble ecqe relg bly ly rel o lcble. o fcle e bly ly of le- fzzy-oel-be corol ye eber fco coo rooe o roce oe lck rce for olery coeo. L-be bly coo re erve g e Lyov-be roc o gree e ye bly. lco ele gve o llre e er of e rooe roc.. roco Sye bly of e fzzy-oel-corol ye eevely e for y yer. Florg bly rel ere obe o gree e ye bly be o e Lyov-be roc. e y of e fzzy-oel-be corol ye e S-fzzy oel []-[] ly or role o crry o e bly ly. e S-fzzy oel offer geerl yec freork o reree e oler l o fcle e ye ly e coroller ye. []-[] bc bly coo e for of ler r eqle L ere erve o gree e bly of e fzzy-oel-be corol ye. y rg e e ecee rle beee e fzzy oel fzzy coroller rele bly coo ere erve. Frer rele bly coo c be fo [5]-[]. Sle- fzzy coroller offer beefcl fere c be leee by crocoroller or gl Correog or: H.K. L Dvo of Egeerg Kg' College Loo Sr Loo WC LS UK E-l: k-keg.l@kcl.c.k cr receve Se. 7; ccee 8 y 8. coer o ece e eg flebly loer e leeo co. goo lerve o be e log fzzy coroller []-[] vro lco. Hoever cole yc of e lg cvy ke e ye bly ly ffcl. o or ffcle ll be fce for vegg e le- fzzy-oel-be corol ye. Oe e zero-orer-ol ZOH ll kee e corol gl co rg e lg ero ve e corol gl cge e lg. rel coy ll be roce o e ye kg e ye yc ore colce. e bly vego []-[] oly e re coo-e or cree-e fzzy-oel-be corol ye ere cocere. Coeqely e e le- fzzy corol ye re coere e bly coo []-[] co be le. o e o e eece of e ZOH e coroller eg crero c e fzzy oel fzzy coroller re e e ecee leg o rele bly rel c o be le. o vege e bly of ler le- corol ye ecror roc [] rooe o crry o e bly ly. y roerly rereeg e ler le- corol ye ecror for [] e coy roce by e le- cvy c be le. [] e bly ly of e o-feebck le- fzzy corol ye vege by rocg eqvle ye. e ye ecee coo-e ye rg e lg ero ll ve e lg. o vege e ye bly e yc of e ecee coo-e ye e yc of e ye e lg ve o be e erely. e ly crre o be o e o ye rg e lg ero e lg c be ee e ly qe eo. e o-feebck le- fzzy corol ye [] gree o be ble f ere e eroc e-vryg olo o e of bly coo. e bly coo re o L for e olo co be olve by kg vge of e effecve cove rogrg ecqe. bee o [] e ecror rereeo offer oel roc o vege e ye bly of ler le- ye. Hoever e oler le- ye re cocere le o coervve bly ly rel e ye olery ffcly o be coere. e ecror rereeo [] eloye o vege e bly of le- erl-eork-be corol ye [] by e e or. e olery of e oler c be le g e erble crcerc of e S-fzzy oel. 8 FS

erol Jorl of Fzzy Sye ol. o. Je 8 Hoever e o e lg cvy e fvorble roery of rg e e ree beee e fzzy oel coroller []-[] co be eloye o rel e ye ly rel. er e ye bly of e le- fzzy-oel-be corol ye vege. e ecror rereeo [] eloye o vege e ye bly. e rbck leg o coervve bly ly rel [] rg e bly ly lleve. e o ecror rereeo e crcerc of eber fco oe free rce re roce o roce bly ly rel. Sbly coo re erve g e Lyov-be roc eree L for c c be olve effecvely erclly g cove rogrg ecqe.. Fzzy oel le- fzzy coroller le- fzzy-oel-be corol ye fore by coo-e fzzy oel le- fzzy coroller roce.. Fzzy oel Le be e ber of fzzy rle ecrbg e oler l. e - rle of e follog for le : F f D D f HE ere α fzzy er of rle correog o e fco fα α...... ove eger; re e ko co ye rce reecvely; e ye e vecor e vecor. e ye yc re efe ere [ ] μ k μ for ll f μ f L μ f k f μ k f L μ k f ko oler fco of fα. μ f α e gre of α α eber correog o e fzzy er α. ol be oe e gre of eber re cer f e oler l bec o reer cere.. Sle-D Fzzy Coroller le- fzzy coroller fzzy rle ege be o e fzzy oel of e oler l. e - rle of e le- fzzy coroller of e follog for: le : F g D D g HE < 5 β ere fzzy er of rle correog o e fco g β...... β ove eger; e feebck g of rle o be ege.... eoe lg e ; eoe e co lg ero. e ferre o of e le- fzzy coroller gve by < 6 ere for < [ ] for ll 7 k μ g μ g L μ g 8 μ k g μ k g L μ k g oler fco of μ g e ko gre of eber correog o e fzzy er β. c be ee fro 6 c ol co vle for <.. Sbly ly eco e ye bly of e le- fzzy corol ye fore by oler l e for of e le- fzzy coroller of 6 ll be vege. e follog ly re eoe reecvely for brevy. Fro 7 e ve e roery c e rg e bly ly. Fro 6 e le- fzzy coroller c be rereee e follog for. β 9 Fro 9 e ve e follog roery c ll be e ler. β

H.K. L E.W.S. C: Sbly ly of le- fzzy-oel-be corol ye e ye bly of e le- fzzy corol ye ll be vege be o e follog Lyov fco ce. ere σ σ ere. ll be o eqly ol e > > c le e yoclly bly of e le- fzzy-oel-be corol ye. Fro 6 e ve ere > ove clr. W e roery e ve. e o roery fro e ve 5 ere... rbrry r. Fro [] e ve e follog. 6 ere. Le.... Fro 6 e ve 7 Fro 5 7 e ve 8 Fro 9 Fro 8 9 e fc leg o e ve ere Le. e ere e clr vle of c >.... Fro e ve Fro c be ee c le e yoclly bly of e le- fzzy-oel-be corol ye e < < <. Le

erol Jorl of Fzzy Sye ol. o. Je 8 for.... Fro e ve Ξ Ξ Ξ Ξ ere Ξ 5 Ξ 6 Ξ 7 y Scr colee o e follog eqly. ere W < eqvle W < 8 Ξ Ξ Ξ Ξ c be ee fro 8 9 W <.... Slrly fro e ve W W < ere W Fro c be ee < f W <....... Frerore e roery of 7 ol e c eqvle o e follog.... 5 ol be oe e eqle of 5 re o L coo e o e eece of e er. W e roery > e coer e follog eqly ζ ζ ζ ζ ζ > ζ ζ 6 ere ζ o-zero ove clr. Fro 5 6 e olg of e follog L ly e f olg of 5 ζ ζ... 7 e bly coo of e le- fzzy corol ye re rze e follog eore. eore : e le- fzzy-oel-be corol ye fore by e oler l e for of e le- fzzy coroller of 6 yoclly ble f ere e co o-zero ove clr > ζ c >... co rce c e follog L ol: > ; > ; > ; 9 7. e feebck g re efe.... erk : e bove ly vl f verble. eferrg o e eore f ere e olo o e bly coo eore le. ee re e > < ffce coo for o be o-glr r o gree verble.. lco Ele lco ele o blzg cr-ole vere el [5] g e rooe fzzy coroller ll be gve eco. Se e ycl eqo of e vere el o e cr [5] gve by 8 F l co Fl co gl l co J l l co 9 F l co J l l F J l gl co J l J l l co ere eoe e glr lcee r e glr velocy r/ of e el fro vercl reecvely eoe e

H.K. L E.W.S. C: Sbly ly of le- fzzy-oel-be corol ye lcee e velocy / of e cr reecvely g 9.8 / e ccelero e o grvy. kg e of e el.8 kg e of e cr l. e leg fro e ceer of of e el o e f J l / kg e oe of er of e el ro e ceer of F.95 // F.756 /r/ re e frco fcor of e cr e el reecvely e force le o e cr. e obecve o eg e rooe fzzy coroller o corol e oler l c ey e. e oler l c be rereee by fzzy l oel o fzzy rle [5]. e - rle gve by le : F HE for e ye yc re ecrbe by [ ] F / F l / F l / F J l / ere ; gl / gl / gl / F / Fl co π / / π gl co π / / F l co π / / F J l / π l / l co π / / J l / J l / J l l ; ; J l l co π /. e eber fco re efe μ 7 π / 6 7 / 6 e e π μ μ. ; ; Se o-rle le- fzzy coroller ll be eloye for e oler l. e rle re of e follog for le : F HE < e le- fzzy coroller efe 5 ere e eber fco re efe μ.8.8 μ μ. e Se e o eore. ζ e ob [88.9898.979.57.9] [5.9.678.559.67]. ele e [ 5 5]. W foro coerg e ve c offer e loer er bo 5 5 5 5 reecvely. Coeqely for y lg e vle of o or before e e lg e rge of 5 5 for. c be o foro ere e fco of e coo of.55. > e le- fzzy coroller of 5 ll be eloye o corol e oler l of 8 o. Fg. o e ye e reoe of e le- fzzy corol ye er e l ye e coo of π π for [ reecvely. 6 ] c be ee e oler l c be blze by e le- fzzy coroller. e corol gl of e le- fzzy coroller re o Fg.. eferrg o fgre c be ee corol gl ee gl c vle el co rg e lg ero. 5. Coclo e ye bly of e le- fzzy-oel-be corol ye bee vege. le- fzzy coroller bee rooe o corol e oler l. e o e Lyov-be roc L-be bly coo ve bee erve o gree e ye bly of e le- fzzy-oel-be corol ye. lco ele bee gve o llre e effecvee of e rooe roc. ckolege e ork ecrbe er blly

erol Jorl of Fzzy Sye ol. o. Je 8 ore by gr fro Kg College Loo. eferece []. kg. Sgeo Fzzy efco of ye lco o oelg corol EEE r. Sy.. Cyber. vol. c-5 o.. 6- J. 985. []. Sgeo.. Kg Srcre efco of fzzy oel Fzzy e ye vol. 8. 5-988. [] C.L. Ce.C. Ce C.K. Ce ly eg of fzzy corol ye Fzzy Se Sye vol. 57 o 6. 5- Jl. 99. [] H.O. Wg K. k.f. rff roc o fzzy corol of oler ye: bly e eg e EEE r. Fzzy Sy. vol. o.. - Feb. 996. [5] K. k. ke H.O. Wg Fzzy reglor fzzy oberver: ele bly coo L-be eg EEE r. Fzzy Sy. vol. 6 o.. 5-65 998. [6] W.J. Wg S.F. C.H. C Fleble bly crer for lgc fzzy yc ye Fzzy Se Sye vol. 5 o.. 6-8 Jl. 999. [7] E. K e roce o rele qrc bly coo of fzzy corol ye EEE r. Fzzy Sy. vol. 8 o. 5. 5-5. [8] oog L glg Zg e roce o H coroller eg be o fzzy oberver for -S fzzy ye v L oc vol. 9 o. 9. 57-58 Se.. [9].C.. eer E. ção.. vellr O rele L-be eg for fzzy reglor fzzy oberver EEE r. o Fzzy Sye vol. o. 5. 6-6 Oc.. [] C.H. Fg.S. L S.W. K L. Hog C.H. Lee e L-be roc o rele qrc blzo of -S fzzy corol ye EEE r. o Fzzy Sye vol. o.. 86-97 Je. 6. [] E. Fr. Sere J.. cr ob le- blzo of ler ye: ely roc oc vol..-6. [] H. Ky. ck H corol for le- oler ye ecrbe by kg-sgeo fzzy ye Fzzy Se Sye vol. 8 o.. -5 Dec.. [] H.K. L F.H.F. Leg Deg blzo of le- erl-eork-be corol ye EEE r. Sy. Cyber r : Cyberec vol. 6 o. 5. 995-5 Oc. 6. [].S. oo. rk W.H. Ko.S. Lee Dely-eee rob blzo of cer e-elye ye. Jorl of Corol vol. 7 o..7-55. [5].J. Z.. S ly eg of fzzy rece-eol oberver fzzy fcol oberver Fzzy Se Sye vol.. 5-6. r r/..8.6.. r..8.6.. -..5.5.5.5.5 5 e ec -. 6 8 e ec - - -6-8 - r/ - - -6-8 - Fg... - -.5..5..5..5..5.5 e 6 ec 8 e ec 6 8 6 Fg. b.. 6 8 e ec Fg. c. for.

H.K. L E.W.S. C: Sbly ly of le- fzzy-oel-be corol ye 5 9 8 9 8 7 7 6 6 / 5 / 5...6.8...6.8 e ec - 6 8 e ec Fg... Fg.. Sye e reoe of e le- fzzy-oel-be corol ye er ffere l ye e coo. 6 6 5 5.5..5..5..5..5.5 e ec - 6 8 e ec Fg.. Corol gl of e le- fzzy coroller for e oler l ffere l ye e coo.

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