Solution manual for chen

Solutions Manual for Linear system Theory and Design.

Solutions Manual for Linear system Theory and Design

e4y6L z

2, t kr) Ltrtza.y (6) e4 g 1 Merr/*rtto-_

4 (h)

{ n* ,*Vtut< / = / _ lo "-, _i.fcfu ,Vr.rrZV

o*4

2' Z 8<tn t<-

AIH ,t4 d j-*rt2^?6 t< o, d4! ;./e.r/ /-,r-/ rtaa /-Uza, 4; )z{

11 h u, 27te) = H (e, tr) * // ( u, zo) r'.' - 4(4,.7o)

H {u, xe) = 2" ll ( I Y") ,.iuoL n7'/,t"

L tJ (t) 4f v

6 a t = f:,' :,';:)' [::,':, ::; ]

4 - t : i t ( t ) c f ( t ) t y G ) : I i 4 ( t - t )

t 1 ' { ( t t r ) = | + { ( i )Bzca<- /k) " 0

{ltt = /

| ,t, =:

Q = o f : t / t ) = o , t ( f l d + 7 G ) ) a t/ r t + r ) = o , t ( | r { k ) )

B z e ' u a - { ( t ) = a h o s t < t '

d l z + +

t ( t ) = o , f / * t s i < 2{ (c) = o.J' 7 t; o,5) = a,7f /* z t t< J

z 3 t < J

J * t < 4

-o < t < // < r 1 2

'f/r'ttt t*< 4a.e.

J:+ I , ,|

'r= xr-(fi *r,)

t, = [:J ft t, =

t r = u r / t t ' t , l l - -

, , r - [ 1

A u na4//T/a4 Thtt4 A-t= A' az.(

A A'= A A'' - Ir, Oo ar, orctr/t& /*

4 ( 1 o - t t 1 - 1,t ; ) ofu ,- D q-,t*, * r!' :i,':.^:i ' t' :' ::' , : ^' t ::i" I J

= lT il,-lj ) arr[t't,-)'l(/,,tttA+) UL-4);tLtLl L) x l

A tii l= [if J=^,fi; 1

li'J t;; I hJ

[LLLL]\l

fiAu Acxv du itt<rta_.e /12e_ rtaf t/

1 4 = O, ^Alon a Ol) = la n d,At * 1tA', olr)

er4 A =o n ah e.i41"ta-/'tz' , orr zl;

,lr-A r0

f/u4 t< u*t- aa,u*z

Aal A a ut tar{a-,

-"t ,l

( u t ' e ) t

, f ( e t t

-oeJ''

i " , t l t , , * i ,

) : J e J " = , , ) r r 3 F r r l l ,E*r,l fu.a

, ax ctztt t'+r.ftLa

8 = o , f ( e i t - 2 e t ' * e t ) / a t = 4 e ) ' - r , r e J t - 2 , f e "

f c = 3 e c + J E t c - e ) i 71ua Bc -/,"4r2

-e o " '

( t l l = , x c ? 4 , 4 + " ' + d n - , 4 o - '

f U ) = F o r 1 3 , 4 r , * / i r n A ' ' t

ca.cy'at*L fU)fU) =7(A)t@ a'"4(,

f ,

f , c

]t

t 1 '-2c

)o

t

t 4

/Vapaatn-tfu */Zox /4 )k?r1-{-/af./a* a.4 /* Qtf

h t t r S n , = J t t ) ' ' 2 h t - ) i t l > + 3 t l 2 = - 1 i l t r n / , = 3 ( z )( r ) - i t S , f h , = Q

* t ' @ , / B I W*of

: tt?/'+ttY z7u<h-d^'

P

,) z

J , 3 |

[ '

l -l :ll::J .[:"'1,.8]

/ 2

At = X, Ua A mrrL eke(

ut*ft (A) = n, ,*/L r-rVd;u h > n ,

$ n > lrt - ,t/r" A'A /4 t xn eu/ "c/Ud.4

t r*-,r-.r, t+a/.c

0,ti"'"-c)4* (t-z) I" -

l { ! , , , n = o , r { l i , ! n o z o , r

l i r l ^ " , , o , f 2 r , l i t ! o " r ' ' , t Lft* t4 'r"rr/ t<<.f 1 4 nyiLZ.

-, 6'aa7k*-,@ y'(r-t1' rAno.ry

, c4 4q4

Z r = t 2 , z , t ' t z r = t ' , = , ,

4.4d,

( f r + n r r " ' r r - Tlr('t 4( ia/"r

Ttu

4 a z € - t ; v / r 1 r 4 / / 4 2 2 a / ' d - r T f u ,

/4'e cer4 *? A/A.{atr

t * 1 - r o t , L l , j

[ * ] ' l , l " , t L - t l

- < r Z t ( Z t * t t

/ d

I:: :J

r, =[": :]., ,l:J r, = G t t

-z 'r t ? L '

s - t 3 s t z

t,t{ tA,uy dq

/4ou.ja ,ci p+c{4^z J.26, ei,.i(-

i t t S = c ( s - E - A ) - t t =

* , [ " p " b r , t - , r < J l , 6 r r - , r - - *

" R n - r b j

t R n - - , b r o r R r b = o

l - L i t o , t , - h r r - 2U4/T atz

o P t b = , : b = a

t - R , b = c A h f , t , " 6 = o + c A l = o:

= e't tr, (e) - xJa) a-, ( "e r rr.

Jo

= e't z, to) r j- arb)

"'t (utt

,Lr P |to,t) = Xtt) ('x''ro) Ak)

L Q, (te,to)

' f t x a ,

4 u { r o e ) = o a * /

.].2' ,ft

a ) '

t +

Q,q,

f,,,

', to, to)

.I

J t

- r(,

(t' 't) 't)

er (,t t-Ak)) = * (rArc,tI f4, _ ,qtu)

= dtt I un' (,t r - 4 (o) ) ,a,t J

= 4ef eArt dt f g'Att AU ('t t- A/4)

co-Tfr {ruruftaa alfan, i til = P[() 7 (t) t"*(

ftau.t /atrr" Q2 *-fittt-Ftei'

ft *l t q * V,u6+, a SflBO tf&{z.

/ k ) , r , 7 - ; i ; ir't=J tSietT ==fifi.

- 2 0

/ a,v ,pt, ,-/rta*L htL = +,8 ?rltt 2.2

, = 1 " r , 1 1 - , '

Lt 6 '; J Poti4* e'he

7lr4.z ,& Qdr,rt ///t4 S n laa a7il-6'/t

b4d A&t, / &t a u1^e4t4, dv 2-/,2'*'ai4d

di 4"f Tb4 g l/4 'oa.4 s aa4 kl ,a P&ih* ,L/4.rrl, ( Mle+y Cs)

A

2 2

ax zafl ulleft fu tediZt" e&/4,).Oxzz,

:b 'ea/a e4rxazit*.

n , r t o ) = - t ' * '

.f,

2 3

afaaZofiza

el4/G.L 6

, e(C) = l u*Trollollc

.f (0) t / rar "-h"'*aU

"t*"

6,5 fo, d4 st<.G n*.^6;* n P&lt*6.t.

an nea( lt'J ,rt a4 a/nu,q/xl*( ){ra

4 a r o f f ' ' r t cf J , I I = f I r f 3 n J f

, I oirt,-,

) ) - I ( I '^") )

6,q Tfu oG,A ,f^"aftA &, Pa^r4&*, e s

at,lqetal 6

['iJ=L^; :,]L;Jr[',]'

t l = E t t , [ : , ) fh) lz tz4f.Lr//a,14 aal

I";""4 )4^otoh,r e*Z/"xe ad tB ftB

Zre n b' d/ /**" $ t's"+os a"1

A1 -<to/t*<z'/ -?fe n e-,d/a/(

X = U, ?,ril:, t'it, P.,tf, P,'il,lE

-J it f - /u,e.Uera/2

du run',al Tfu; effdtr;-' t) ,4d

,!tr e^/;4-uv/14d .ttr -ltJ TA./ t1r<,uta

,z<et u(4;,a;* qrAeZ;rr*

sEA Zaa<.;.ao>, xna.Gl 4 At

t+4 eatTaE-ol * Paa/4.r1 U,/6 a'

ntc, to) = [ | ' eo't

t'l oo

"'t 'L'1

L d e r t t r - c o ' ) JtJ'z en7>r.6

C * t *o ) , (a e o t (.t ro\

J aa.l

, f t e - t 1

/ v A L ; ; " - ' ) = , P e r r f t r / , r 2

t

- ' * ( z ) = o o h u

# r-' o, =

=^rrf,:,:::,'.

i tet = - A't+t / Gt & frX, b1 = - A'(tt X, /+t 7a,ht^f i6 fa*'apc*<

f^r/"/n

f, xl ,a= - xirtt Ak) Ttuo ar< 4nr<, X'rc) = X-'1il ,8,'eri'=y/t) + lt, z) = X Gt X-'(.)

7' 3 toe uo-c (6.+aS a; aal a.a 44

laer{ 6 Ae- ,tt-/./"Z;* ; Pazl(c', f t "

f - t - t : o o l f - _ t t o 1

l l y ' , , - t - , l l o l - \ = o

1 4 o ' , 0 L l l t ; \

l o u ' r * o J L D t J AJAt,t4( D1 ena 2 *t ry con+6nf,

wd = E - 1 o + J 5 n = t ' t 2 o J )

S - E d 0 ; t L a ; 0 d ; o n 7 ' ;] = u 4 2 ( s t

ft'- Ire.tvaf.^ /uz4fa$ o/ uU)

tt'.o ^At / (4 &

744/4 &t ausllat<l ,a naU,aTvla't /

L

- t - 6 t I -t

( s + r ) 5 1 t / 2 )

J J

-d,cl, = f

t /'c*f t

n *-{ Nz l,lt+q.lt pa /11

/r&&4^r fr- e4ona, T-fu/td rkpttta 7.H1

&t// )ud l&

' J 4

F"l ,la4 pila -2 e,4 -J - ,r'4

/*(o) = t

2 J t - g s r I

-J

7

-&o t/ac!{r ; Prta/,4*,, 8, +

I r i t t J

= r t ( z l ? S 1 t

Salr<l^luf, A'l- i.-€e ,',5 au^d (z) e'/

% "* /tz114o/ €fu nr*q /'<Az 5 r/te

hz-tu64z.la Fứt c.* /tnau

O, k4 A'u.v A.V B Gl 7 ct7 A{sl *? A

&r, = &o r &,s' "( df / t* "Lct'v

/ o la-*?lt

+ p ' + = - o , 2

' 4 t

-rhz auynr ,ti// fa-v4 oV q "ay'uzoc,

-h4 nzzo( A ,z&-tkq

tr'-L@

4t a,o^c-n -Li dy +ntfoq r:_ d zz,

t ' 7 + t s 1 - s t ' r r t - 4 s ) r ( s " " 0 r 5 ' & ^ i " B r ! ): FG)

dt y'ul|'yt i,

L r s l - z z ; - 4

SrLdf7r1 : (,r

-*4

?)14 = t

iTLnr dLl ?1 rf'n A.a-c&o *f o6V ^./rr.r-i

i = z t z + t - + t - s n z f [ ; l

q : x + t l - r - r t l t ; ]

M.*

R/, R'/;tz.

( s ) - - - - 4 ?

-5 - < J ' J ' r '

&t p cla "1 i,rss)

- l s - f ' , { , , r 0 ) o

t s = o

' f;/tc) -ti

Ttna ,i 'a? ar-4'uru 4"'/ D(t) ta

az&.a-/ ^il/t ,/t = S (ttz ft,,tu 'n ( f '+z)'

i ncf u,uz,/ a-et d1 ce+v<lrztt/.,7r ?t'zt i<+f /<

= [';:,it'.',J'''4 ' j'

Thad gtt 'rLa*< 4 = z, ,'tL : 2 ' B eaaat yt ryL

+ 7

, r l r O ' , - i t , J + z

o I o t , o ) t

ty& m,*tA/.4 ? a:z cz1ruZ

' + , 7 - rj ,/ i - t r , r - t z

I r

' 1 3 - 4 3 : - o , ) - ,

| , Tlrt4d IAJ c.+f az<.fov t4

4 a 4 d , = , 1 , ) - !

rg

A-'(st LB) at<4 A'/kl Hu)

au c14oV/ ad A,z cei+z4fe?4l&./ t(L rrra&f /4

ataytA d f4 o, rfu 4il.,6e, n.ry/

N'd = [': :-, ] , 4 ") ' Nt'|kt n1','fl, ,' l

ctp.tt'}4?-l, r,i l', [',",J"

" J

' [ ' , : l ' r [ " " J "

oe dt,af ,-{ ,"i( 6a44 oT ofp -"/a/r/ cz

t upa{ t}e ,ru

{,4 4rilr"4"( f"-,

AG) Drtr,'ri::r:::;::t,

, l

L a t l r 2 s i z l e+

Ino nlo; 4r ; nr,d

/

-r' l'1,1 n d:izLl