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CS Assignment 5

The document discusses various mathematical concepts related to systems and equations, including properties of matrices and observability in control systems. It presents equations in matrix form and explores the conditions for a system to be completely observable. Additionally, it includes examples and calculations relevant to the discussed topics.

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megapalak
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13 views10 pages

CS Assignment 5

The document discusses various mathematical concepts related to systems and equations, including properties of matrices and observability in control systems. It presents equations in matrix form and explores the conditions for a system to be completely observable. Additionally, it includes examples and calculations relevant to the discussed topics.

Uploaded by

megapalak
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF or read online on Scribd
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K=O ‘is Bssume A sol" of x =bo tbit +b ¢*+ - tbe t*4 ~ — —_ @® peje 2 bo + + 3144 hep eee eee i eae FEriisore 707 , Rris = abo tob)t +apratt+- -- ——G 7 A bue soluHon. [Hs = ns. on d@® oa ai oe al eee ye bon aioe ee eB IZ Mey =/ ixraeto Ob ete peed ene : pee +)= 2-40), __- ois EA. = Ce Now {| T fk properties of SaETO . = ° eae | @ st are sr ed Ley= dO ya = (nt) Beco e ([s*4+55+6) pacers cy'CS) bo AES @&. 10d \= matt) alt) = xley= eq @ be come EA Ser (e traced = uct), p mat) + s(t) +5794) 420 t= ULE) Q % 963 (4S IE ENCED, tu (t) et TA mobi ® Eom, 21 Ct “a | 1 tt) pn) se oer) os 4 Beet |=] o 6 | 2045 ef uit) 4 23 U4) cs os AJ | %3 (4) leg] 7 ~+ foorm eq. ©, BYCS es i eu = XCD 35%105) +41 CS) = CS) = Tokig a hw "i : Wt ey Ce) re 3g itt) = 2X2 Ct) ; use lenrow, Banco ( p>) tami cea Ve) he written AS aoe [x12 1 re notte) | = 3 CED aoa (e rc nonarte BE ia Ares 1D st435 +3 AS= Byostysst eres. = = recSa 8, CSE oe =Stsy Ky CS). + = ae oe oe #1CSD 1 2! aa ROS SP-4 257438 +1 Exes Zi —— = s a aa eres -@ : From eg” © $265) + 257K GS) 435 104) eae = RG) crevlening << ET Hit )4 2K) (4) 42 Ct) + eI A= dd fet , A(t d= X2Ce) ~% Kol) =xalt) =x). AS (y= xy bt) Hence » 29" ©, , D42%3 (4) + 3X24) HET). — __%3 (+) = out) ~8%2 C+ D=2%K 9/4) 49°C) a este) Ss <8 [ou [oad [=] 0 eet SO 33 CE 4 meee x CE 0 : So = + 3X2 (+) + 3164) =VCo. —efp—2quation in mabix form Coc ¢#) pect) = Pee eee ae L7 eh eis Also Find g (). 5 ely ef ere a eed —O_} staal = | ayer eo BUN (er on) 2 | S23 lel Secenoneaneems jeer _ = = Stasy2 = (s+2CsH). z C43. 19 a ees ee (say = peyayess ye ieee 2 — ts és _ SF 3ny tse Se CstzyCsH (SR) SH) L a T fa (sx -a} dalee “wadividual truersce .\ s+3 PB 5 | WES MTD absent Le = s Cst1) saa 7 Epis ci st—Ay - 3 Sen ate ef eo —7t an —7t -E Siem tare 2 cues -e - aS ee sn = 2 ~. Qe = Ls ag |= poe determinant ve @ nce J@c| #0% Jue Rak of Oe =n=2, A system ic Cowpletely obseywable jf aud | Only IF ne rojak of Hae composi Fe : poaa tri X Qo Ls. ye od where, : mg T\R=T =p ie ne me POR) J pe ah ase order oF +e sysiem iS _ ise seme Qo = E a ue el) ards cos leee | ail > \l ' e 1H ane deteyminowt of Qe \Qol = 2 3 = O1 [ eS on a =zer0 pune Pomak oF Qo F eae ystems ls ot observable Wernce +tre

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