NORMAL POSITIVE LINEAR SYSTEMS AND ELECTRICAL CIRCUITS
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1 EEKYK 8 Zzyt 5 o XIV duz KZOEK łyto Uvrty o chology NOM POSIIVE INE SYSEMS ND EEI IUIS Sury h oto o orl otv lctrcl crcut troducd d o thr cc rort r vtgtd Nw tt trc o otv lr yt d lctrcl crcut r rood d thr rort r lyzd It how tht otv lctrcl crcut wth dgol tt trc r orl or ll vlu o rtc ductc d cctc Kyword: orl otv lr yt lctrcl crcut NOMNE DODNIE UKŁDY INIOWE I OWODY Strzcz W rtyul zrooowo ojęc dodtgo owodu ltryczgo orz rzlzowo cjl włośc dodtch ułdów owodów ltryczych Wyzo ż dodt owody ltrycz z dgoly crz tu ą zwz orl dl wzytch wrtośc rzytcj ducyjośc ojośc Słow luczow: ułd orly dodt lowy owód ltryczy INODUION dycl yt clld otv t trjctory trtg ro y ogtv tl tt r orvr th otv ortht or ll ogtv ut ovrvw o tt o th rt otv yt thory gv th oogrh ] Vrty o odl hvg otv hvor c oud grg cooc ocl cc ology d dc tc h oto o cotrolllty d orvlty hv troducd y Kl 5 ] d thy r th c coct o th odr cotrol thory ] h cotrolllty rchlty d orvlty o lr yt d lctrcl crcut hv vtgtd 7 5 7] h ytotc tlty o otv tdrd d rctol lr yt h ddrd ]
2 8 Kczor h cc dulty d tlty o otv lctrcl crcut hv lyzd 8] d otv yt d lctrcl crcut wth vr tt trc ] h tlty o cotuou-t d dcrt-t lr yt wth vr tt trc h vtgtd ] h rducto o lr lctrcl crcut wth colx gvlu to lr lctrcl crcut wth rl gvlu h codrd ] Stdrd d otv lctrcl crcut wth zro trr trc hv vtgtd 9] d th orl otv lctrcl crcut hv troducd ] I th r th orl otv lr yt d lctrcl crcut r vtgtd h r orgzd ollow I cto o rlr cocrg otv lr cotuou-t yt r rclld So rort o th trr trc o otv lr yt r rtd cto Norl otv lr yt r lyzd cto Norl otv lr lctrcl crcut r troducd d vtgtd cto 5 ocludg rr r gv cto h ollowg otto wll ud: - th t o rl ur rl trc M - th t o I - th - th t o - th t o rl trc wth ogtv tr d Mtzlr trc rl trc wth ogtv o-dgol tr dtty trx PEIMINIES whr odr th cotuou-t lr yt x x t u u t x x u y x y y t r th tt ut d outut vctor d Dto ] h lr yt clld trlly otv y t t or y tl codto x d ll ut hor ] h lr yt otv d oly M u t t x t d Dto ] h otv lr yt or u t clld ytotclly tl l x t or ll x t hor ] h otv lr yt or u t ytotclly tl th trx Hurwtz d oly ll coct o th chrctrtc olyol
3 Norl otv lr yt 9 r otv or dt I ] W hll codr th otv yt wth th trx o th or or hor ] h otv yt wth 5 ytotclly tl d oly 5 or Dto ] h otv yt clld rchl t t ] or y gv l tt x thr xt ut x t ro zro tl tt x to th l tt x Dto ] rl trx u t or t t ] tht tr th tt x t x clld ool ch t row colu cot oly o otv try d th rg tr r zro hor ] h otv yt rchl th trx ool h ut t t t d t 7 x u t x t t ] 8 tr th tt x t o th yt ro x to x t x h otv yt rchl t t ] d oly M dgol d h lrly ddt ool colu Dto 5 ] h otv yt clld orvl t t ] owg th outut x y t d th ut u t t ol to d th uqu tl codto hor 5 ] h otv yt orvl t t ] th trx ool O t d t 9
4 Kczor NSFE MIES OF POSIIVE INE SYSEMS h trr trx o th otv lr yt gv y ] I whr th t o rtol trc hor I th trx M gv y 5 ytotclly tl Hurwtz d th ll coct o th trr trc I ] I ] r ogtv Proo I Hurwtz d th th tr o th vr trx ] - I r rtol ucto wth ogtv coct hror d th ll coct o th trr trx r ogtv h roo or lr dul Exl odr th trr ucto o th otv yt wth ] I th c ug d w ot
5 Norl otv lr yt 9 9 ] ] ] I 5 h trr ucto l-h c t zro 5 z z r gtv tr ccllto o th zro z wth th ol w ot It y to chc tht ] 7 th ] ] I 8 I th c w hv 9 5 r r ] 9 d r r hror th tdrd r cotrolll ut th r uorvl odr th SISO gl-ut gl-outut otv lr yt wth gv y 5 d
6 Kczor It y to chc tht r ] t z z z th zro th root o d root o d o th trr ucto hor I th ol th I ] d r th t lt o zro o qul to t ol Proo It wll-ow tht hold th th zro d ol ccllto occur It h oly t lt o zro o qul to t ol Now lt u codr th SISO otv yt wth gv y 5 d It y to chc tht r hor t ucto I ] 5 th ol d z z z th zro o th trr 7 I ] th t lt o zro o 7 qul to t ol Proo h roo dul to th roo o hor r ] 8 NOM POSIIVE INE SYSEMS odr th trr trx o th or N d
7 Norl otv lr yt whr N ] th olyol trx d d th lt coo dotor o th or d Dto h otv lr yt wth clld orl vry ozro cod ordr or o N dvl wth zro rdr y th olyol d h orl yt r tv to th chg o thr rtr ] Dto h tt trx o th lr yt clld cyclc t l olyol qul to t chrctrtc olyol dt I ] h l olyol rltd to t chrctrtc olyol y ] D whr D th grtt coo dvor o ll ordr or o th trx I ] hror d oly D hor h trc d dd y 5 r cyclc Proo y Dto d th trc d r cyclc d oly th grtt coo dvor o ll ordr or o th trc I ] I ] r It y to tht th or corrodg to th rt colu d th -th D row o th trx I ] d to th rt row d th -th colu o th trx I ] r qul to hror D d th trc d r cyclc hor h otv lr yt wth th trc d dd y 5 orl or y d
8 Kczor Proo y Dto th otv lr yt wth dd y 5 d y orl vry ozro cod ordr or o th trx N I ] d dvl y th olyol dt I ] t q Z j j j th or o th trx Z wth t q colu h t wll-ow ] tht th q-or o th trx q P q q q row d j j j q t Z PQ gv y q q Z j j j Q q j j j 5 q Not tht th or o th trc d r ddt o Ug 5 or th trx I t y to tht t vry ozro cod ordr or dvl y ] d dt I ] c y hor th trx cyclc hror th otv lr yt wth d y orl Exl odr th otv lr yt wth th trc g to ccout tht d w ot or c c c c c c d dt I ] 7 N I ] c c I ] d 8 c c d c c 9
9 Norl otv lr yt 5 whr c c c c c c c c c c c c c c c c hror th otv lr yt wth orl c c c c c c c c Not tht th trc 5 or r qul d hv th dgol or d 9 dg ] I th rtculr c hor h th ollowg or hor h otv lr yt wth d y orl 5 NOM POSIIVE INE EEI IUIS odr lr lctrcl crcut cood o rtor cctor col d voltg currt ourc th tt vrl th coot o th tt vctor x t w choo th voltg o th cctor d th currt th col Ug Krchho lw w y dcr th lr crcut trt tt y th tt quto whr x x t u u t x x u 5 y x 5 y y t r th tt ut d outut vctor d Dto 5 ] h lr lctrcl crcut 5 clld trlly otv th tt vctor ut x t d outut vctor u t t y t t or y tl codto x hor 5 ] h lr lctrcl crcut 5 otv d oly M d ll 5 h trr trx o th lr lctrcl crcut dcrd y 5 c lwy wrtt th or Dto 5 h otv lr lctrcl crcut clld orl vry ozro cod ordr or o N dvl y d
10 Kczor Exl 5 odr th lr lctrcl crcut how o Fg wth gv rtc ductc d ourc voltg Fg Elctrcl crcut o Exl 5 y Owód ltryczy dl rzyłdu 5 Ug th h thod or th lctrcl crcut w ot dt d 5 whr t t r th h currt d 5 h vr trx 5 h ll otv tr Fro 5 w ot dt d 55 whr 55 Not tht d 5
11 Norl otv lr yt 7 th th trx h th or o th trx dd y 5 d or 5 th or o th trx I oth c th lctrcl crcut otv h codrto c ly xtdd to -h lr lctrcl crcut Followg ] lt u codr th lr lctrcl crcut how Fg wth gv rtc 8 ductc 8 cctc 5 7 d ourc voltg 8 Fg Potv lctrcl crcut y Dodt owód ltryczy Ug Krchho lw w y wrt th quto h quto c wrtt th or du u dt d j j j j j j 8 57 dt whr d d dt u u 58 u u u u 5 u
12 8 Kczor dg c h trx 8 M dgol d ytotclly tl d 85 hror th lctrcl crcut otv or y vlu o th rtc ductc d cctc d ro hor w hv th ollowg ortt thor hor 5 Potv lr lctrcl crcut wth dgol trx M d orl or y vlu o th rtc ductc d cctc ONUDING EMKS h oto o orl otv lctrcl crcut h troducd d o cc rort o th cl hv vtgtd Nw tt trc o th otv lr yt d lctrcl crcut hv troducd d thr rort hv lyzd hor d It h how tht th otv lctrcl crcut wth dgol tt trc r orl or ll vlu o thr rtc ductc d cctc hor 5 h codrto hv llutrtd y urcl xl h codrto c xtdd to rctol lr yt d lctrcl crcut cowldgt h tud hv crrd out th rwor o wor No S/WE// d cd ro th ud or cc y th Polh Mtry o Scc d Hghr Educto EFEENES ] tl E Mchl : r Syt rhur oto ] Fr ld S: Potv r Syt: hory d lcto J Wly & So Nw Yor
13 Norl otv lr yt 9 ] Kczor : ytotc tlty o otv rctol D lr yt ull Pol cd Sc ch vol 57 o ] Kczor : hrctrtc quto o th tdrd d dcrtor lr lctrcl crcut Poz Uvrty o chology cdc Jourl: Elctrcl Egrg o ] Kczor : hrctrtc olyol o otv d l-h lctrcl crcut Elctrcl vw vol 9 o ] Kczor : otructlty d orvlty o tdrd d otv lctrcl crcut Elctrcl vw vol 89 o 7-7] Kczor : otrolllty d orvlty o lr lctrcl crcut Elctrcl vw vol 87 o ] Kczor : Dcoulg zro o otv dcrt-t lr yt rcut d Syt vol -8 9] Kczor : Ml-h otv lctrcl crcut Elctrcl vw vol 9 o 8-89 ] Kczor : Norl otv lctrcl crcut IE rcut hory d lcto vol 9 o ] Kczor : Polyol d tol Mtrc Srgr-Vrlg odo 7 ] Kczor : Potv D d D Syt Srgr-Vrlg odo ] Kczor : Potv lctrcl crcut d thr rchlty rchv o Elctrcl Egrg vol o 8- ] Kczor : Potv lr yt d lctrcl crcut wth vr tt trc Elctrcl vw vol 9 o 9-7 5] Kczor : Potvty d rchlty o rctol lctrcl crcut ct Mchc t utotc vol 5 o -5 ] Kczor : chlty d cotrolllty to zro tt or tdrd d otv rctol dcrt-t yt Jourl Euroé d Syt utoté JES vol o ] Kczor : o o tdrd d rctol lr yt d lctrcl crcut wth drvtv o thr ut Elctrcl vw vol 9 o - 7 8] Kczor : Scc dulty d tlty o otv lctrcl crcut rchv o Elctrcl Egrg vol o ] Kczor : Stdrd d otv lctrcl crcut wth zro trr trc Poz Uvrty o chology cdc Jourl: Elctrcl Egrg o 85-8 ] Kczor : Vctor d Mtrc utoto d Elctrotchc WN Wrw 998 Polh ] Kczor orw K: ducto o lr lctrcl crcut wth colx gvlu to lr lctrcl crcut wth rl gvlu Murt utoto Motorg vol o ] Kczor orw K: Stlty o cotuou-t d dcrt-t lr yt wth vr tt trc Murt utoto Motorg vol o - 5 ] Kczor ogow K: Frctol r Syt d Elctrcl rcut Stud Syt Dco d otrol vol Srgr 5
14 Kczor ] Klth : r yt Prtc Hll Eglwood l Nw Yor 98 5] Kl E: Mthtcl dcrto o lr yt SIM J otrol vol o ] Kl E: O th grl thory o cotrol yt Proc t Itr ogr o utotc otrol odo ] Kl J: otrolllty o Dycl Syt Kluwr cdc Pr Dordrcht 99 8] Wolovch W: r Multvrl Syt Srgr Nw Yor 97 Pro dr h ż duz KZOEK lyto Uvrty o chology Fculty o Elctrcl Egrg ul Wj 5D 5-5 łyto
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Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1866 Colby College Catalogue 1866-1867 Colby College Follow this and additional works at: http://digitalcommons.colby.edu/catalogs
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