4 7002

ITL . noitcnuf refsnart kcabdeef etats

ITL

)1( uB+xA = x)2( uD+xC = y

)u,t(x, 1 :

)s(uB+ )s(xA = )0(x )s(xs :

)s(uB1)AIs( + )0(x 1)AIs( = )s(x

1L[1)AIs(

])3( tAe =

Lt [

0

)(g) t(f]

)t(g)t(f

)s(g)s(f =

1

1)AIs( = )s(f )s(uB = )s(g 3

1L[)s(uB1)AIs(

]=t

0

d)(uB)t(Ae

)t(x :

)0(xtAe = )t(xtupni orez

ecnopser

+t

0

d)(uB)t(Aeecnopser etats orez

)4(

.

, ) ( 0 = )0(x,

)s(u)s(H = )s(uB1)AIs( = )s(x

)s(H )snoitcnuf refsnart( u x u x.

ji))s(H(, , s.

u y. 2 )s(x

)s(uD+ )s(xC = )s(y)s(u]D+ )s(HC[ =

=[D+B1)AIs( C

]

)s(G

)s(u

)s(G , -xirtam noitcnuf refsnart u y.

2

C )s(H

D

)s(x)s(y )s(u

G

)s(y )s(u)s(G

+

s/I

A

C B

D

)s(x)s(y )s(u+

H

G

+

) ( . )s(G . ) snoitcuf refsnart(.

3

Ky rG F+uy

-

y = r y y .

r y:

]yKrF[ G = yrFG = y)KG+I(

)5( rFG1)KG+I( = y

: kcabdeef etats

g

s/I

A

)s(y=)s(x )s(u+ b

= )t(x[

3 11 3

]

A

+ )t(x[

10

] b

)t(u

)t(x = )t(y

2 = 1 4 = 2. !

4

y rg+ux=y

-

k

= k. 5[2k 1k

]

rg 1)kg +I( = y

b 1)AIs( = )s(g

= y(kb 1)AIs( +I

1)rb 1)AIs(

=[)AIs(

(kb 1)AIs( +I

1])rb

rb 1]kb + )AIs([ =

)s(rb 1))kb A( Is( = )s(y,

rb +xA = ykb A = A

=[

3 11 3

][2k 1k0 0

]=

[2k 3 1k 1

1 3

],

)8 1k 2k3( +s)2 1k( + 2s = |A Is| }2k ,1k{ .

4 = 1k 371 = 2k 2i 1 = 2,1. , )(.

, r, 4 , t

= )t(xt

0

rbtd)t(Ae

5

=

0

e

[3 11 3

])t(

td

[10

]r

=51 [

35

]r

, r51 = 1y r53 = 2y. , , ) I =6 F( . , 3/5 = F

= )0(x[

55

]

6 4 2 0 2 4 62

0

2

4

6

8

01

2x

1x

enalp esahp

01 8 6 4 2 06

4

2

0

2

4

6

emit

1x

emit fo noitcnuf sa

01 8 6 4 2 02

0

2

4

6

8

01

emit

2x

denibmoctupni orezetats orez

uB+xA = x

)0(xtAe = )t(xtupni orez

ecnopser

+t

0

d)(uB)t(Aeecnopser etats orez

, 0 = u

tAe = )n(xA

)1 n(x

) ( )t +tn , tn( nu

+ )1 n(xtAe = )n(xt

0

nuBd)t(Ae

6

: t0

eA(t)d = A1(eAt I)

x(n) = eAt A

x(n 1) +A1 (eAt I)B B

un

7