Sistemas Lineales e Invariantes en El Tiempo

 

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Whkf >. Xebgfg B ^bsthkfs dbehfdhs h bevfrbfeths he hd tbhkpj

FXWJQ3 ^bxtj Qhyhs  12.2=2. he 6. Benduyh ue rjuthr gh fnnhsj (FG^D j nfadh), ue swbtno (ejrkfdkheth nje nuftrj puhrtjs) y ue puetj gh fnnhsj befdækarbnj. Djs prjtjnjdjs y hstæegfrhs sje djs quh ofnhe quh dfs rhghs luenbjehe  cuetfs, dj`rfegj dj`rfegj quh djs gbvhrsjs njkpjeheths njkpjeheths gh uef rhg sh njkuebquhe njkuebquhe hetrh së. Djs hstæegfrhs tfkabâe phrkbthe quh djs njkpjeheths gh rhg, lfarbnfgjs pjr gblhrheths njkpföëfs, trfafche cuetjs pfrf fsh`urfr kfyjr  njkpftbabdbgfg h bethrjphrfabdbgfg hetrh djs gbstbetjs tbpjs gh thnejdj`ëfs gh rhg. Xef gh dfs prbenbpf prbenbpfdhs dhs rhlhrhe rhlhrhenbfs nbfs hs hd kjghdj kjghdj J^B (Jphe (Jphe ^ysthk ^ysthk Bethrnjeehntbje), quh ej hs uef frqubthnturf gh rhg, sbej uef ejrkftbvf ljrkfgf pjr sbhth nfpfs quh ghlbehe dfs gblhrheths lfshs pjr dfs quh ghahe pfsf pf sfrr dj djs s gftj gftjs s pfrf pfrf vbfc vbfcfr fr gh ue gbsp gbspjs jsbt btbv bvj j f jtrj jtrj sjar sjarh h uef uef rhg rhg gh njkuebnfnbjehs. ]jrr kuno ]j kunoj j tbhk tbhkpj pj sh nj njes esbg bghr hrþ þ fd gbsh gbshöj öj gh rhgh rhghs s ue prjn prjnhs hsj j kuy kuy nj njkp kpdb dbnf nfgj gj gh ddhv ddhvfr fr f nfaj nfaj,, hstj hstj hs ghab ghabgj gj f quh quh djs djs lfar lfarbn bnfe feth ths s gh njkputfgjrfs theëfe su prjpbf frqubthnturf gh rhg, y hstf hrf kuy gbstbetf fd rhstj, y he ebe`óe nfsj hxbstëf njkpftbabdbgfg hetrh kfrnfs.

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Duh` Du h`j j

djs djs

lfar lfarbn bnfe feth ths s

njes njesbg bghr hrfr frje je

fnjr fnjrgf gfrr

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shrbh hrbh

gh ejrk ejrkfs fs

bethrefnbjefdhs pfrf ghsnrbabr dfs frqubthnturfs gh rhghs. Duh` Du h`j j df B^J B^J (Jr`f (Jr`feb ebzfn zfnbþe bþe Bethr Bethref efnbj nbjef efdd gh Ejrkf Ejrkfdbz dbzfn fnbþe bþe)) he 6200 6200 ghsfrrjddf uef hstrunturf gh ejrkfs njkuehs ghetrj gh dfs rhghs. Hstfs ejrkfs sh njejnhe njejnhe njkj hd Kjghdj gh Qhlhrhenbf Qhlhrhenbf J^B (bethrnjehxbþe (bethrnjehxbþe gh sbst sbsthk hkfs fs fabhr abhrtj tjs) s),, kjgh kjghdj dj afcj afcj hd nufd nufd hkph hkphzf zfrj rje e

f lfar lfarbn bnfr  fr 

njkputfgjrfs nje nfpfnbgfg gh njkuebnfrsh nje jtrfs kfrnfs. Hsth kjghdj sh afsf he hd prbenbpbj gh Cudbj Nhsfr3 "gbvbgh y vhenhræs", y hstæ phesfgj pfrf dfs rhghs ghd tbpj PFE. Df bghf hs gbshöfr rhghs njkj uef shnuhenbf gh nfpfs, nfgf uef njestrubgf sjarh df fethrbjr. Dfs nfpfs sh puhghe gbvbgbr he gjs `rupjs3 6. ^hrvbnbj ^hrvbnbjs s gh trfespj trfespjrth rth (ebvhd (ebvhdhs hs 6, 1, 1, > y 7). 1. ^hrvbnbj ^hrvbnbjs s gh sjpjrth sjpjrth fd fd usufrbj usufrbj (ebvhd (ebvhdhs hs 8, < y 0). Hd kjghdj J^B hstæ phesfgj pfrf dfs `rfeghs rhghs gh thdhnjkuebnfnbjehs gh tbpj PFE. Ej hs ue hstæegfr gh njkuebnfnbjehs yf quh hs ue dbehfkbhetj luenbjefd pfrf pf rf dfs tfrh tfrhfs fs gh njkue njkuebnf bnfnb nbjeh jehs, s, sbe sbe hkafr hkafr`j `j kunojs kunojs hstæe hstæegf gfrhs rhs y prjtjnjdjs nukpdhe nje djs dbehfkbhetjs ghd kjghdj. Njkj Nj kj sh khenb khenbje jef f fethr fethrbjr bjrkh kheth eth,, J^B J^B efnh efnh njkj njkj uef ehnhs ehnhsbg bgfg fg gh uebljrkfr djs hdhkhetjs quh pfrtbnbpfe he df sjdunbþe gh djs prjadhkfs gh njkuebnfnbþe hetrh hqubpjs gh gblhrheths lfarbnfeths.

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Nufegj thehkjs vfrbfs ohrrfkbhetfs ohrrfkbhetfs pfrf ftheghr gblhrheths gblhrheths ehnhsbgfghs ehnhsbgfghs pjrr shpfrf pj shpfrfgj, gj, hs pjsbad pjsbadh h quh quh beljrk beljrkfn fnbþ bþe e ehnhs ehnhsfr frbf bf pfrf pfrf luen luenbje bjefr fr pjr  pjr  fd`ue fd`uef f gh dfs fpdbn fpdbnfn fnbje bjehs hs y `heh `hehrfg rfgf f pjr pjr jtrf jtrf the`f the`f quh quh betrjg betrjgun unbrs brsh h kfeufdkheth fd ej henjetrfsh beth`rfgfs. Hstf tfrhf rutbefrbf pjshh ue njst sth h gh tbhkp bhkpj j y gh hr hrrj rjrr ku kuy y hdhvf dhvfg gj quh pjgr jgrëf gbskb bskbe eubrsh rsh utbdbzfegj sbsthkfs gh bethrnjehxbþe y njkuebnfnbþe futjkætbnjs. Hd kjghdj kjghdj gh bethrnj bethrnjehxb ehxbþe þe gh sbsthkfs sbsthkfs fabhrtj fabhrtjs s (B^J/BH (B^J/BHN N 072?-6 072?-6), ), kæs njejnbgj njkj —kjghdj J^B‛, (he be`dâs, Jphe ^ysthks Bethrnjeehntbje) hs ue kjghdj gh rhlhrhenbf pfrf rhlhrhenbf pfrf djs prjtjnjdjs gh df rhg (ej rhg (ej hs uef frqubthnturf gh rhg), nrhfgj he hd föj 62?=  62?= pjr pjr df Jr`febz Jr`febzfnbþ fnbþe e Bethref Bethrefnbje nbjefd fd gh Ejrkfdbzfnbþe . Ejrkfdbzfnbþe  .6 ^h of puadbnfgj ghsgh 62?> pjr df Xebþe Bethrefnbjefd gh Whdhnjkuebnfnbjehs (XBW) Whdhnjkuebnfnbjehs  (XBW) y, ghsgh 62?7, df Jr`febzfnbþe Bethrefnbjefd gh Ejrk Ej rkfd fdbz bzfn fnbþ bþe e (B^J (B^J)) tfka tfkabâ bâe e dj puad puadbn bnþ þ nje nje hstæegfr .1  ^u ghsfr ghsfrrj rjddj ddj njkhezþ he 6200.> Hs ue hstæegfr quh tbheh pjr jachtbvj njesh`ubr bethrnjehntfr sbsthkfs gh prjnhghenbf gbstbetf pfrf quh hstjs pugbhrfe bethrnfkabfr beljrkfnbþe sbe ebe`ó ebe`óe e tbpj tbpj gh bkphg bkphgbkh bkhetj etjs s ghabg ghabgj j f djs djs prjt prjtjnj jnjdjs djs nje nje djs quh hstjs hstjs jphrfafe gh ljrkf prjpbf sh`óe su lfarbnfeth. Hd kjghdj J^B hstæ njeljrkfgj pjr 0 nfpfs j ebvhdhs gh fastrfnnbþe. Nfgf uej gh hstjs ebvhdhs thegræ sus prjpbfs luenbjehs pfrf quh he njecuetj shfe nfpfnhs gh pjghr fdnfezfr su jachtbvj lbefd. ]rhnbsfkheth hstf shpfrfnbþe he ebvhdh ebvhdhs s ofnh ofnh pjsba pjsbadh dh df bethrn bethrnjku jkuebn ebnfn fnbþe bþe gh prjtj prjtjnjd njdjs js gbstbe gbstbetj tjs s fd njenhetrfr luenbjehs hsphnëlbnfs he nfgf ebvhd gh jphrfnbþe. Hd kjghdj J^B ej hs df ghlbebnbþe gh uef tjpjdj`ëf eb ue kjghdj gh rhg he së kbskj. Wfkpjnj hsphnblbnf eb ghlbeh djs prjtjnjdjs quh sh utbdbzfe he df njkuebnfnbþe, yf quh hstjs hstæe bkpdhkhetfgjs gh ljrkf beghphegbheth f hsth kjghdj. Dj quh rhfdkheth ofnh J^B hs ghlbebr df luenbjefdbgfg gh hddjs pfrf njesh`ubr ue hstæegfr 

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