(67,7 $QQpH MHXGL QRYHPEUH

'6 5pJXODWLRQ $QDORJLTXH $, ± 3DJH

(67,7 $QQpH MHXGL QRYHPEUH

$,

'HYRLU 6XUYHLOOp

5(*8/$7,21 $1$/2*,48(

'XUpH K PLQ VDQV GRFXPHQW FDOFXODWULFH QRQ SURJUDPPDEOH DXWRULVpH

([HUFLFH SRLQWV

5pVRXGUH O¶pTXDWLRQ GLIIpUHQWLHOOH VXLYDQWH HQ XWLOLVDQW OD WUDQVIRUPpH GH /DSODFH

= +

+ \ W

GW W G\

GW W

\

G DYHF \ = \ =

'RQQpHV = − ⁺

 S) S I GW

W

/ GI

[ ]

D H S

/ ^DW

= −

([HUFLFH SRLQWV

6RLW O¶DVVHUYLVVHPHQW G¶XQ V\VWqPH GRQQp SDU OD ILJXUH FL GHVVRXV

'RQQHU O¶H[SUHVVLRQ GH OD IRQFWLRQ GH WUDQVIHUW GX V\VWqPH < S ; S 'RQQHU O¶H[SUHVVLRQ GH OD IRQFWLRQ GH WUDQVIHUW GH O¶HUUHXU ε S ; S

([HUFLFH SRLQWV

6RLW XQ V\VWqPH + GRQW OD IRQFWLRQ GH WUDQVIHUW HVW OD VXLYDQWH

S E S D S N

+ = + +

'RQQHU O¶DOOXUH GH OD UpSRQVH LQGLFLHOOH VXLYDQW TXH + SRVVqGH S{OHV UpHOV XQ S{OH UpHO GRXEOH RX GHX[ S{OHV FRPSOH[HV FRQMXJXpV 2Q VXSSRVH LFL TXH OHV SDUDPqWUHV D HW E VRQW UpHOV QRQ QXOV HW TXH OH SDUDPqWUH N VRLW UpHO VWULFWHPHQW SRVLWLI

< S

* S

+ S

; S



ε S

'6 5pJXODWLRQ $QDORJLTXH $, ± 3DJH ([HUFLFH SRLQWV

6RLW OH PRQWDJH pOHFWULTXH FL GHVVRXV FRPSUHQDQW XQH UpVLVWDQFH 5 HQ SDUDOOqOH VXU XQH FDSDFLWp & HW XQH UpVLVWDQFH U

'RQQHU OD IRQFWLRQ GH WUDQVIHUW + S HQ /DSODFH GH FH V\VWqPH G¶HQWUpH H W HW GH VRUWLH V W 'RQQHU O¶H[SUHVVLRQ GX JDLQ VWDWLTXH O¶RUGUH HW OD FODVVH GX V\VWqPH

2Q VXSSRVH LFL TXH U 5 NΩ HW & µ)

0HWWUH + S VRXV OD IRUPH VXLYDQWH HW GRQQHU OHV YDOHXUV GH D E HW N

S E

S N D

S

+ +

= +

'RQQHU OD YDOHXU GX JDLQ VWDWLTXH GX V\VWqPH

'RQQHU O¶H[SUHVVLRQ GH OD UpSRQVH LQGLFLHOOH GX V\VWqPH 7UDFHU O¶DOOXUH GH OD UpSRQVH LQGLFLHOOH GX V\VWqPH

'RQQHU O¶H[SUHVVLRQ GX JDLQ G\QDPLTXH HQ G% HW GH OD SKDVH GX V\VWqPH 7UDFHU O¶DOOXUH GX JDLQ HW GH OD SKDVH GDQV OD SODQ GH %RGH

2Q UpDOLVH OH ERXFODJH j UHWRXU XQLWDLUH GH FH V\VWqPH

'RQQHU O¶H[SUHVVLRQ GH OD IRQFWLRQ GH WUDQVIHUW GX V\VWqPH ERXFOp 'RQQHU O¶RUGUH GX V\VWqPH

'RQQHU OH JDLQ VWDWLTXH GX V\VWqPH

'RQQpHV /¶LPSpGDQFH FRPSOH[H G¶XQH FDSDFLWp & HVW

S

&

=_F =

([HUFLFH SRLQWV

4XDQG SHXW RQ GLUH TX¶XQ V\VWqPH HVW VWDEOH "

4X¶HVW FH TX¶XQ V\VWqPH SUpFLV "

4X¶HVW FH TXH OD UDSLGLWp G¶XQ V\VWqPH "

4X¶HVW FH TX¶XQ V\VWqPH OLQpDLUH "

(QRQFHU OHV PpWKRGHV SHUPHWWDQW GH FDUDFWpULVHU OD VWDELOLWp G¶XQ V\VWqPH

$QQH[H 7DEOH GH WUDQVIRUPpHV GH /DSODFH XVXHOOHV SDJH VXLYDQWH 5

H W & V W U

'6 5pJXODWLRQ $QDORJLTXH $, ± 3DJH

7DEOH GHV WUDQVIRUPpHV GH /DSODFH XVXHOOHV

I W ) S I W ) S

W 8

D S

D

W S

(

⁻

)

−

Q W^Q

SQ

( )

^W

δ

( )

[

^{] W}

]

] W H

I

W ]

VLQ −

=ω −^{− ω} ω



 + +

=

ω ω

S ] S

S )

W

H⁻D

D S+

τ W

H⁻

− ^S

(

^{+τ S}

)

( )

^Q

W

Q H

Q W

τ

− τ

−

−

(

+τ ^S

)

^Q

τ

τ H W

W ₋



 

 +

− ^S

(

^{+τ S}

)

τ τ

τ ^{H W}

W− + ^{− S}

(

^{+τ S}

)

τ

τ H W

D ₋



 

 −

+ ^S

(

^++DτSS

)

( )

[

^{ω ϕ}

]

ω − −

− −

= ⁻ ] W

] W H

I

W ]

VLQ

DYHF 











−

= −

] DUFWDQ ] ϕ















 + +

=

ω ω

S ] S

S S )

DYHF] VLQ ωW

+ S ω

ω H^−DWVLQωW ^{ω +}

(

^ωS+D

)

FRVωW

S S

ω + ^H−DWFRVω^{W ω +S}

(

^+SD+D

)

[

^{H W D H W E}

]

E D

−

− −

−

(

^{+D S}

)(

^+ES

)

[

^{DH W D EH W E}

]

D E

−

− −

+ − ^S

(

^{+D S}

)(

^{+E S}

)

FRVωW

− 

 +ω S S

τ

τ

τ W

H

D W ₋



 



 − −

+ ^S

(

^++DτSS

)

τ ^{H W} τ

D

W+ − − ^{− S}

(

^++DτSS

)

VLQ W H^−DW ω

D S+ ω +

ω FRV W

H^−DW ω

D S

D S

+ +

+ ω