Question

Solve the following State - Space equa [4] = [:] 4 cs] + [ ]ule given: c= [1 o x(0)=( 17 t and u(t)= unit step function 1 I= Identity matrix Find: D= [o] 2 0 (t) = L [(sI-A)'] @ ylt)

Answer 1

Siven) Given. TI -31 *214) This is similar to sa AXA BU :10615-(1) o pet' = Z'[65 -83"] :- fobere Is iterhiny matrix) > 43-)= 60 :1 (3:3 Als (SA) (GIA) det A AH, CE-A) = n(3), Adj I-A) - Adi t3 Ad (SI-) = $T-A) pel (ILA) = c. labla adobe a) € 12 19 ad-be Coladbe = (+3)-(-1) (2) 180-A) = s'+3542

adj (SIA) ( IST - A) : S+3 $35+2 +33+2 | EL I 3² +3312 3735+ Apply inverse Lit to individual terms > clementing in an obs] Bugis sing panel tanton] -(3) - (TV) is locaten) =zet net (: '[*)= cat] silloin' su sta] f(5) - 7" (sic) - -2 * Cinture et de o 72684_143 {i tomay co] och langes in the -26 de sons) = 1** - 1741842)

substitute can 0;0,0,0 in eqo For Izet azt & et Ostia ACT- A) t 26 2e2+ = {CIA) Le cze question - yet) = cх4) T.Dult) att ZIR+ ZSR - 1. ZIR = zero impele repone = olt) XO) Ľ ZsR= zero take response = T (0) Bucs] 24 It -26 - >AU XCD)Lee at -t ze ze -at rt ee-e 1 Tº fino (:)) Given X60) [ t -2t ze -e te 2t e ut Le 24 2e + 25 - 2 e -t -2t 1 3e ze t at - 3620 ZIR=

268) [6 zsty to sste s+18+ 21 Lou 003) + 3435+2 10: UU nu muellplying above mahires. l.' B on marathing above matico : 8-): uero O+- . (8735423 of 1333+2) L sto se neo7 fonction lede ZUR = Leather in substitute egin oso in eqin uce):- herwisele.sk porn te ck3)= a Ht) ] @ ,

Sut eq@ in qo y(t) = C LE+DU a yu= cxle) D-Co) = y(t) = calt) = 1199 ering wsing matrix multiplication matrix By =lleet- e 2 + H2A)) +(O)(zet 2) ya) = fece 4 me jucts please do like, any quaries comment, 'will rudd solution

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