New Stability Criteria for a Class of Stochastic Systems with Time Delays

Transcription

1 IANG Iio Jou of Appid Mhic 46: IJAM_46 7 Nw Siiy Cii fo C of Sochic Sy wih i Dy Ji W Ac I hi pp h po of poi iiy i ivid fo c of y ochic i-dy y Howv o d fw uho hv coidd h iiy yi po of y y h i i of h pp i o fi p By couci ui ypuov-kovkii fucio d ui dcopoiio chiqu ov uffici iiy codiio oid which u ou coidd y i h -qu poi iiy I ddiio p i iv o how h coc d ffciv of h oid cii h u wi pp i h fuu Id poi Siiy i-dy Gy Sy ypuov-kovkii ucio Dcopoiio chiqu I I INRODCION i w kow h i dy i i y pcic y uch couicio coic d chic y i dy fquy occu i viou ii y which d o ociio iiiy o pfoc ddio of h y [] o ic o ccou of iid dwidh h cu wok of cu poi i dy vi wok couicio hfo h udy of y wih i dy h co ujc of iiv ch civiy d u of u hv oid [-] I [4] d o h ypuov iiy hoy d h i i iquiy ppoch h uho h popod h iiy cii of dyic y wih uip i-vyi dy d oi ucii I ddiio ochic odi o h ipo ffc i y fi of cic o iduy fo p cooic cooy d ifoio y c [-] hu h udy of ochic y h co vy ipo d uch ici io h focud o h iiy po of ochic y i c y p o ow y ipo u hv pod [3-8] I [5] h uho hv povidd v uffici cii o u ochic y i h -qu poi iiy Pcicy du o viou o uch h ck of ifoio ouc o ukow ucii w wi o ih c hic od of ojc o poc iy d w c o oi o p of y ccuy So w hv o vu h p of y I houd poid h wh h p ihd y y u h y wi co y uci h ch i uppod y h Nio Nu Scic oudio of Chi No 39 d h Ky Pojc of Nu Scic oudio of ducio Coi of H Povic No 6B Ji W i wih Schoo of Mhic d Siic Ay No iviy Ay 455 PR Chi -i: wi@ico y [9] Hc i i cy o udy h iiy po of y y Howv h fw u o hi po [9-4] I [9] h uho hv udid h poi iiy fo h y ochic y wih diiud dy d iv p d hv popod v iiy cii which u h y y i p-o poi iiy Ipid y h ov wok w cocd wih h poi iiy po fo c of y i-dy ochic y i hi pp i w couc ui ypuov-kovkii fucio h ui dcopoiio chiqu of h coiuou i-covd of y i w wi oi wo ov iiy cii o u h y y i h -qu poi iiy I h d of hi pp p i pd o iu h ffciv of h oid iiy cii Noio: h upcip "" p h po R d R do h -diio ucid pc d h of ic do h ucid o fo vco o h pc o of ic h oio X Y pcivy X Y wh X d Y yic ic h X Y i poiiv i-dfii pcivy poiiv dfii Moov P do cop poiiy pc wih fiio C [ ];R ifyi h uu codiio do h fiy of coiuou R -vud fucio o [ ] [ ]; R do h fiy of C [ ];R : -u oudd vi -vud do II PRIMINARIS AND PROBM ORMAION Coid h foowi y ochic i-dy y: d A B d dw [ ]; R wh A d B y uci ic A B d y of A d B cd Advc oi puicio: 4 My 6

2 IANG Iio Jou of Appid Mhic 46: IJAM_46 7 [ ] { A ˆ : i j } [ ] { B ˆ : i j } h coiuou i-covd of A d B Aˆ d Bˆ whid diiic ic of A d B ] d ] h [ u-covd of [ houhou h pp w k h foowi upio d dfiiio o y : A H : R R R R d ifi h oc ipchiz codiio A if h i c fo iy y H : R R R h foowi iquiy ho: y y c[ y Dfiiio [9] Sy i poiy i qu if fo [ ]; R d whid ˆ B ˆ [ ] ic A [ ] c dc ; C uch h up h i Now u ioduc h foowi i picu which wi ud i h poof of ou i u [9] If A i y i ] i u-covd of y h [ fo iy whid i A [ ] w hv wh ˆ A ˆ A A A 3 ˆ A ˆ i whid u of ˆ ˆ [ ] ] [ i u-covd of d i ui y u [3] N i of ppopi diio h fo y vco y d ε > w hv Ny y N Ny III MAIN RSS AND PROOS I h foowi ho wo ov iiy cii wi divd which u y i h -qu poi iiy ho 3 If h i c uch h k k 3 wh k k h fo [ ]; R w hv k up H i h uiqu poiiv ouio of h foowi quio 3 k k 33 h i y i poiy i qu Poof i w ioduc ypuov-kovkii fucio: V 34 h y ui h wk ifiii opo o h jcoi of y w hv V ˆ A B ˆ ] c [ 35 By d i foow h A ˆ 36 Advc oi puicio: 4 My 6

3 IANG Iio Jou of Appid Mhic 46: IJAM_46 7 d B ˆ By upio A w hv ] c[ Suiui of io 35 w c V [ ] [ ] 39 i Iô diffi fou d ii oh i fo o > d h ki pcio w hv V V up [ d V [ ] ] u u du up 3 3 o 3 d 3 oi h dfiiio of k k w c oi h k V up [ k k ] 3 f k k h f k Sic f f k k d f wh 3 ho 33 u hv uiquy poiiv ouio hfo w hv h i up V k k up which ipi h y i poiy i qu hi cop h poof of ho 3 Of cu h iiy ciio 3 h o ho Wh i o h o qu o h iv w wi o cofi whh y i h -qu poi iiy By h ii hod w c ov hi po [] i y h whid y of y c wi d [ A ˆ dw B ] d 33 Sic [ A ˆ B ˆ ] Advc oi puicio: 4 My 6

4 IANG Iio Jou of Appid Mhic 46: IJAM_46 7 dw 34 So w ioduc h foowi fucio [ A ˆ B ˆ ] H dw 35 [ A ˆ B ˆ ] [ A ˆ B ˆ 39 ] o h whid y of y c wi d [ A ˆ H B ] d dw [ ]; R 36 o pov ho 3 h foowi i cy d 3 o [ ]; R fucio H ifi k wh H k k up up 4 4 h ov Poof i oi h dfiiio of H w hv H [ A ˆ B ˆ ] 37 dw 38 Oviouy By upio A w dw 3 Coii 38-3 oh d oi h dfiiio of k k h w c oi H k k 3 i 3 d ii oh i w c up k k H uho u u H du du 3 u du up Siiy 33 u du 34 Suiui of io 3 d oi h dfiiio of d of 3 i copd h 37 ho h poof By 36 d 3 w wi p oh ciio of poi iiy i h qu fo y Advc oi puicio: 4 My 6

5 ho 3 If h i c uch h 3 35 wh 3 h fo ]; [ R w hv [ up ] up 36 H i h uiqu poiiv ouio of h foowi quio 37 h i y i poiy i qu Poof i foowi h ii i of h poof of ho 3 w hv V [ ] H 38 i Iô fou d ii oh i h ki pcio d oi h dfiiio of H w V V V [ ] up ] [ up 39 h Sic 3 d If 35 ho 37 u hv uiquy poiiv ouio hfo w c V [ up ] up h i 36 ho h poof of 3 i copd IANG Iio Jou of Appid Mhic 46: IJAM_46 7 Advc oi puicio: 4 My 6

6 IANG Iio Jou of Appid Mhic 46: IJAM_46 7 Rk 3 If A A B B y wi co h foowi diiic ochic y wih i dy: A B d d [ ]; R dw 33 A B d y ui h ii ho of ho 3 d ho 3 w oi h foowi iiy cii fo y 33 Cooy 3 If h i c uch h A A p p wh p p B B h fo [ ]; R w hv k up H i h uiqu poiiv ouio of h foowi quio A A p p 333 h i y 33 i poiy i qu Cooy 3 If h i c uch h A A B B q q 334 wh q q B B h fo [ ]; R w hv [ B B up ] B B up 335 H i h uiqu poiiv ouio of h foowi quio A A B B q B B 336 h i y 33 i poiy i qu IV p Coid y ochic i-dy y: d A B 5 d 5 dw [ 5]; R 5 4 wh ; ; d h ow oud d upp oud ic of A d B 5 d c[ 5 i 5 i By ui h po i [9 ] w c ccu d 5587 o 638 Appyi ho 3 o ho3 i i foud h y 4 i poiy i qu V Cocuio I hi pp h poi iiy po h ivid fo c of y ochic y wih i dy By ui h ypuov-kovkii hod Iô diffi fou d dcopoiio chiqu wo iiy cii hv oid h oid cii wi u h y y i -qu poi iiy I ddiio iu p h pd o how h coc d ffciv of h i u h copodi u wi pp i h fuu Ackowd h uho hk h oyou viw fo ho hpfu co d vu uio o ipovi hi pp ] Advc oi puicio: 4 My 6

7 IANG Iio Jou of Appid Mhic 46: IJAM_46 7 RRNCS [] M Mk-Zvi d M Jhidi i-dy Sy: Ayi Opiio d Appicio Ad Nh: Noh-Hod 987 [] K Bouk d Z K iu Diiic d Sochic i-dy Sy Boo MA: Bikhu [3] S Aik Go ou iiy yi of u wok wih dic i dy Cho Soio d c vo 6 o 5 pp [4] J H Pk Rou iizio fo dyic y wih uip i-vyi dy d oi ucii Jou of Opiizio hoy d Appicio vo 8 o pp [5] W J Xio d J i Nov iiy cii fo u y wih uip i dy Cho Soio & c vo 3 o 5 pp [6] R Rkkiypp d P Bui Nw o poi iiy u fo u yp u wok wih diiud i dy Nuocopui vo 7 o 4 pp [7] P Pk A dy-dpd iiy ciio fo y wih uci i-ivi dy I cio o Auoic Coo vo 44 o 4 pp [8] Y Giz V uky d J Shi i Co Diiuio i Dic-i Cood Sy wih Diuc d Noi-Coupd S Ifoio IANG Iio Jou of Appid Mhic vo 4 o pp 5-59 [9] i Siizio of I Swichd Sy wih Ipu i Dy ii vo 4 o pp [] C Kuo d Y J Hu Go Siizio of Roo Coo wih Nu Nwok d Sidi Mod ii vo 6 o pp [] H Kuh Sochic Siiy d Coo Acdic P Nw Yok 967 [] X Mo Sochic Diffi quio d Appicio Chich K: Howood Puihi 997 [3] H Y Q H M X Hu d H Zh Rou poi iiy of ochic i-dy y wih ucii d oi puio Iio Jou of Ifoio Acquiiio vo 6 o pp [4] X Mo Rou of poi iiy of ochic diffi dy quio I Auo Coo vo 4 o 3 pp [5] X io d X Mo poi iiy of ochic dy iv y Sy Coo vo 4 pp 7 8 [6] H J Chu d X Go Rou poi iiy d H coo fo jupi ochic Coh-Go u wok wih id dy Jou of Copuio Ifoio Sy vo 7 o 3 pp [7] W Ch d X u M qu poi iiy of uci ochic dyd u wok Phyic A vo 37 o 7 pp [8] S Y Xu J d X Mo Y Zou A w MI codiio fo dy-dpd ou iiy of ochic i-dy y Ai Jou of Coo vo 7 o 4 pp [9] C H Su d S iu h p-o poi ou iiy fo ochic y wih diiud dy d iv p Appid Mhic d Mchic vo 3 o 7 pp [] C H Su d S iu poi Rou Siiy of Gy Nu Sochic Sy wih Diiud Dy Chi Jou of ii Mhic vo 7 o 3 pp [] C H Su d S iu Rou Siiy of Gy Sochic Noi Sy wih Diiud-Dy Mhic i Pcic d hoy vo 38 o pp [] J J i d C H Su M-qu poi Rou Siiy fo C of Gy Sochic Sy wih Diiud Dy Chi Qu J of Mh vo 5 o 3 pp [3] A id Sochic diffi quio d hi ppicio Nw Yok Acdic P 976 [4] C H Su Rou Siiy of Gy Sochic Dy Sy wih ipuiv ffc Sy Sci & Mh Sci vo3 o5 pp Advc oi puicio: 4 My 6