// Equation de l'observer , papier Wodes, synthse Maia exemple Katz, 12/2009, Belo Horizonte

// equation de l'observer :  z(k)=A z(k-1) + B u(k) + d(k)
// d(k)=F( y(k) ), c'est la fonction qui dpend de l'observateur
// je  donne ci-dessous l'expression de d1(k) jusqu' d9(k)




// initialisation des variables










// on pose d1(k)= d11(k) + d12(k) + d13(k) 
// d11(k) est l'lment qui depend de la sortie y1(k)
// rappel y1 est x3, y2 est x6, y3 est x8

// il faut aussi une variable intermdiaire f11(k) car il s'agit
// d'quations affines

f11(k)=22 * y1(k-6) + 29 * y1(k-7) + 35 * y1(k-9) + 41 * y1(k-10) + 25* f11(k-6);
d11(k)=4*y1(k-4) + 8 * y1(k-3) + 14* y1(k-4) + f11(k);
f12(k)=24 * y2(k-6) + 30 * y2(k-8) + 36 * y2(k-9) + 42 * y2(k-11) + 25* f12(k-6);
d12(k)=3*y2(k-2) + 9 * y2(k-3) + 15* y2(k-5) + f12(k);
f13(k)=24 * y3(k-6) + 30 * y3(k-8) + 37 * y3(k-9) + 43 * y3(k-11) + 25* f13(k-6);
d13(k)=3*y3(k-2) + 12 * y3(k-3) + 16* y3(k-5) + f13(k);


//L[0,1] =  g^1 d^4+ g^3 d^8+ g^4 d^14+( g^6 d^22+ g^7 d^29+ g^9 d^35+ g^10 d^41)[ g^6 d^25]*
//L[0,5] =  g^2 d^3+ g^3 d^9+ g^5 d^15+( g^6 d^24+ g^8 d^30+ g^9 d^36+ g^11 d^42)[ g^6 d^25]*
//L[0,7] =  g^2 d^3+ g^3 d^12+ g^5 d^16+( g^6 d^24+ g^8 d^30+ g^9 d^37+ g^11 d^43)[ g^6 d^25]*


f21(k)=13 * y1(k-4) + 20 * y1(k-5) + 26 * y1(k-7) + 32 * y1(k-8) + 25* f21(k-6);
d21(k)=2*y1(k-5)+f21(k);
f22(k)=15 * y2(k-4) + 21 * y2(k-6) + 27 * y2(k-7) + 33 * y2(k-9) + 25* f22(k-6);
d22(k)=y2(k-1)+6*y2(k-3)+f22(k);
f23(k)=15 * y3(k-4) + 21 * y3(k-6) + 28 * y3(k-7) + 34 * y3(k-9) + 25* f23(k-6);
d23(k)=3*y3(k-1) + 7 * y3(k-3) +  f23(k);

//L[1,2] =  g^2 d^5+( g^4 d^13+ g^5 d^20+ g^7 d^26+ g^8 d^32)[ g^6 d^25]*
//L[1,5] =  g^1 d^0+ g^3 d^6+( g^4 d^15+ g^6 d^21+ g^7 d^27+ g^9 d^33)[ g^6 d^25]*
//L[1,7] =  g^1 d^3+ g^3 d^7+( g^4 d^15+ g^6 d^21+ g^7 d^28+ g^9 d^34)[ g^6 d^25]*

f31(k)=18 * y1(k-5) + 25 * y1(k-6) + 31 * y1(k-8) + 37 * y1(k-9) + 25* f31(k-6);
d31(k)=y1(k)+4*y1(k-2)+10*y1(k-3)+f31(k);
f32(k)=20 * y2(k-5) + 26 * y2(k-7) + 32 * y2(k-8) + 38 * y2(k-10) + 25* f32(k-6);
d32(k)=5*y2(k-2)+11*y2(k-4)+f32(k);
f33(k)=20 * y3(k-5) + 26 * y3(k-7) + 33 * y3(k-8) + 39 * y3(k-10) + 25* f33(k-6);
d33(k)=8*y3(k-2) + 12 * y3(k-4) +  f33(k);


//L[2,2] =  g^0 d^0+ g^2 d^4+ g^3 d^10+( g^5 d^18+ g^6 d^25+ g^8 d^31+ g^9 d^37)[ g^6 d^25]*
//L[2,5] =  g^2 d^5+ g^4 d^11+( g^5 d^20+ g^7 d^26+ g^8 d^32+ g^10 d^38)[ g^6 d^25]*
//L[2,7] =  g^2 d^8+ g^4 d^12+( g^5 d^20+ g^7 d^26+ g^8 d^33+ g^10 d^39)[ g^6 d^25]*

f41(k)=26 * y1(k-7) + 33 * y1(k-8) + 39 * y1(k-10) + 45 * y1(k-11) + 25* f41(k-6);
d41(k)=8*y1(k-2)+12*y1(k-4)+18*y1(k-5)+f41(k);

f42(k)=28 * y2(k-7) + 34 * y2(k-9) + 40 * y2(k-10) + 46 * y2(k-12) + 25* f42(k-6);
d42(k)=3*y2(k-1)+7*y2(k-3)+13*y2(k-4)+19*y2(k-6)+f42(k);

f43(k)=28 * y3(k-7) + 34 * y3(k-9) + 41 * y3(k-10) + 47 * y3(k-12) + 25* f43(k-6);
d43(k)=1*y3(k-1) + 7 * y3(k-3) +16*y3(k-4) + 20 * y3(k-6)+  f43(k);

//L[3,2] =  g^2 d^8+ g^4 d^12+ g^5 d^18+( g^7 d^26+ g^8 d^33+ g^10 d^39+ g^11 d^45)[ g^6 d^25]*
//L[3,5] =  g^1 d^3+ g^3 d^7+ g^4 d^13+ g^6 d^19+( g^7 d^28+ g^9 d^34+ g^10 d^40+ g^12 d^46)[ g^6 d^25]*
//L[3,7] =  g^1 d^1+ g^3 d^7+ g^4 d^16+ g^6 d^20+( g^7 d^28+ g^9 d^34+ g^10 d^41+ g^12 d^47)[ g^6 d^25]*

f51(k)=16 * y1(k-5) + 23 * y1(k-6) + 29 * y1(k-8) + 35 * y1(k-9) + 25* f51(k-6);
d51(k)=3*y1(k-2)+9*y1(k-3)+f51(k);

f52(k)=18 * y2(k-5) + 24 * y2(k-7) + 30 * y2(k-8) + 36 * y2(k-10) + 25* f52(k-6);
d52(k)=4*y2(k-2)+10*y2(k-4)+f52(k);

f53(k)=18 * y3(k-5) + 24 * y3(k-7) + 31 * y3(k-8) + 37 * y3(k-10) + 25* f53(k-6);
d53(k)=6*y3(k-2) + 11 * y3(k-4) +  f53(k);

//L[4,2] =  g^2 d^3+ g^3 d^9+( g^5 d^16+ g^6 d^23+ g^8 d^29+ g^9 d^35)[ g^6 d^25]*
//L[4,5] =  g^2 d^4+ g^4 d^10+( g^5 d^18+ g^7 d^24+ g^8 d^30+ g^10 d^36)[ g^6 d^25]*
//L[4,7] =  g^2 d^6+ g^4 d^11+( g^5 d^18+ g^7 d^24+ g^8 d^31+ g^10 d^37)[ g^6 d^25]*


f61(k)=23 * y1(k-6) + 30 * y1(k-7) + 36 * y1(k-9) + 42 * y1(k-10) + 25* f61(k-6);
d61(k)=5*y1(k-1)+9*y1(k-3)+15*y1(k-4)+f61(k);

f62(k)=25 * y2(k-6) + 31 * y2(k-8) + 37 * y2(k-9) + 43 * y2(k-11) + 25* f62(k-6);
d62(k)=y2(k)+4*y2(k-2)+10*y2(k-3)+16*y2(k-5)+f62(k);

f63(k)=25 * y3(k-6) + 31 * y3(k-8) + 38 * y3(k-9) + 44 * y3(k-11) + 25* f63(k-6);
d63(k)=4*y3(k-2)+ 13 * y3(k-3) + 17 * y3(k-5) +  f63(k);

//L[5,2] =  g^1 d^5+ g^3 d^9+ g^4 d^15+( g^6 d^23+ g^7 d^30+ g^9 d^36+ g^10 d^42)[ g^6 d^25]*
//L[5,5] =  g^0 d^0+ g^2 d^4+ g^3 d^10+ g^5 d^16+( g^6 d^25+ g^8 d^31+ g^9 d^37+ g^11 d^43)[ g^6 d^25]*
//L[5,7] =  g^2 d^4+ g^3 d^13+ g^5 d^17+( g^6 d^25+ g^8 d^31+ g^9 d^38+ g^11 d^44)[ g^6 d^25]*

f71(k)=5 * y1(k-2) + 12 * y1(k-3) + 18 * y1(k-5) + 24 * y1(k-6) + 25* f71(k-6);
d71(k)=f71(k);

f72(k)=7 * y2(k-2) + 13 * y2(k-4) + 19 * y2(k-5) + 25 * y2(k-7) + 25* f72(k-6);
d72(k)=f72(k);

f73(k)=7 * y3(k-2) + 13 * y3(k-4) + 20 * y3(k-5) + 26 * y3(k-7) + 25* f73(k-6);
d73(k)=  f73(k);


//L[6,2] = ( g^2 d^5+ g^3 d^12+ g^5 d^18+ g^6 d^24)[ g^6 d^25]*
//L[6,5] = ( g^2 d^7+ g^4 d^13+ g^5 d^19+ g^7 d^25)[ g^6 d^25]*
//L[6,7] = ( g^2 d^7+ g^4 d^13+ g^5 d^20+ g^7 d^26)[ g^6 d^25]*

f81(k)=10 * y1(k-3) + 17 * y1(k-4) + 23 * y1(k-6) + 29 * y1(k-7) + 25* f81(k-6);
d81(k)=5*y1(k-1)+9*y1(k-3)+15*y1(k-4)+f81(k);

f82(k)=12 * y2(k-3) + 18 * y2(k-5) + 24 * y2(k-6) + 30 * y2(k-8) + 25* f82(k-6);
d82(k)=2*y2(k-2)+f82(k);

f83(k)=12 * y3(k-3) + 18 * y3(k-5) + 25 * y3(k-6) + 31 * y3(k-8) + 25* f83(k-6);
d83(k)=y3(k)+ 13 * y3(k-2) +  f83(k);

//L[7,2] =  g^1 d^1+( g^3 d^10+ g^4 d^17+ g^6 d^23+ g^7 d^29)[ g^6 d^25]*
//L[7,5] =  g^2 d^2+( g^3 d^12+ g^5 d^18+ g^6 d^24+ g^8 d^30)[ g^6 d^25]*
//L[7,7] =  g^0 d^0+ g^2 d^3+( g^3 d^12+ g^5 d^18+ g^6 d^25+ g^8 d^31)[ g^6 d^25]*

f91(k)=14 * y1(k-4) + 21 * y1(k-5) + 27 * y1(k-7) + 33 * y1(k-8) + 25* f91(k-6);
d91(k)=1*y1(k-1)+7*y1(k-2)+f91(k);

f92(k)=16 * y2(k-4) + 22 * y2(k-6) + 28 * y2(k-7) + 34 * y2(k-9) + 25* f92(k-6);
d92(k)=2*y2(k-1)+8*y2(k-3)+f92(k);

f93(k)=16 * y3(k-4) + 22 * y3(k-6) + 29 * y3(k-7) + 35 * y3(k-9) + 25* f93(k-6);
d93(k)=4*y3(k-1)+ 9 * y3(k-3) +  f93(k);

//L[8,2] =  g^1 d^1+ g^2 d^7+( g^4 d^14+ g^5 d^21+ g^7 d^27+ g^8 d^33)[ g^6 d^25]*
//L[8,5] =  g^1 d^2+ g^3 d^8+( g^4 d^16+ g^6 d^22+ g^7 d^28+ g^9 d^34)[ g^6 d^25]*
//L[8,7] =  g^1 d^4+ g^3 d^9+( g^4 d^16+ g^6 d^22+ g^7 d^29+ g^9 d^35)[ g^6 d^25]*


