P],A1′,1,’s’);
lmiterm([3 1 1 N2],B1,C2,’s’);
lmiterm([3 1 1 P],A2′,1,’s’);
lmiterm([3 1 1 N1],B2,C1,’s’);
lmiterm([3 1 1 S11],2/(1-beta),1);
lmiterm([3 1 2 N2],-B1,Cr);
lmiterm([3 1 2 N1],-B2,Cr);
lmiterm([3 1 2 S12],2/(1-beta),1);
lmiterm([3 1 3 P],2,1);
lmiterm([3 1 4 N2],B1,1);
lmiterm([3 1 4 N1],B2,1);
lmiterm([3 1 6 0],(C1’+C2′)*Q^0.5);
lmiterm([3 1 7 P],1,Ad1);
lmiterm([3 1 7 P],1,Ad2);
lmiterm([3 2 2 Pr],Ar’,2,’s’);
lmiterm([3 2 2 S22],2/(1-beta),1);
lmiterm([3 2 5 Pr],2,1);
lmiterm([3 2 6 0],-2*Cr’*Q^0.5);
lmiterm([3 3 3 0],-2*(gama^2));
lmiterm([3 4 4 0],-2*(gama^2));
lmiterm([3 4 6 0],2*(Q^0.5));
lmiterm([3 5 5 0],-2*(gama^2));
lmiterm([3 6 6 0],-2);
lmiterm([3 7 7 S11],-2,1);
lmiterm([3 7 8 S12],-2,1);
lmiterm([3 8 8 S22],-2,1);
%%%%%%%%%%%%%%%%%%1-1-2 , 1-2-1%%%%%%%%%%
lmiterm([4 1 1 P],A1′,1,’s’);
lmiterm([4 1 1 N1],B1,C2,’s’);
lmiterm([4 1 1 P],A1′,1,’s’);
lmiterm([4 1 1 N2],B1,C1,’s’);
lmiterm([4 1 1 S11],2/(1-beta),1);
lmiterm([4 1 2 N2],-B1,Cr);
lmiterm([4 1 2 N1],-B1,Cr);
lmiterm([4 1 2 S12],2/(1-beta),1);
lmiterm([4 1 3 P],2,1);
lmiterm([4 1 4 N2],B1,1);
lmiterm([4 1 4 N1],B1,1);
lmiterm([4 1 6 0],(C1’+C1′)*Q^0.5);
lmiterm([4 1 7 P],1,Ad1);
lmiterm([4 1 7 P],1,Ad1);
lmiterm([4 2 2 Pr],Ar’,2,’s’);
lmiterm([4 2 2 S22],2/(1-beta),1);
lmiterm([4 2 5 Pr],2,1);
lmiterm([4 2 6 0],-2*Cr’*Q^0.5);
lmiterm([4 3 3 0],-2*(gama^2));
lmiterm([4 4 4 0],-2*(gama^2));
lmiterm([4 4 6 0],2*(Q^0.5));
lmiterm([4 5 5 0],-2*(gama^2));
lmiterm([4 6 6 0],-2);
lmiterm([4 7 7 S11],-2,1);
lmiterm([4 7 8 S12],-2,1);
lmiterm([4 8 8 S22],-2,1);
%%%%%%%%%%%%2-1-2 ,2-2-1 %%%%%%%%%%
lmiterm([5 1 1 P],A2′,1,’s’);
lmiterm([5 1 1 N1],B2,C2,’s’);
lmiterm([5 1 1 P],A2′,1,’s’);
lmiterm([5 1 1 N2],B2,C1,’s’);
lmiterm([5 1 1 S11],2/(1-beta),1);
lmiterm([5 1 2 N2],-B2,Cr);
lmiterm([5 1 2 N1],-B2,Cr);
lmiterm([5 1 2 S12],2/(1-beta),1);
lmiterm([5 1 3 P],2,1);
lmiterm([5 1 4 N2],B2,1);
lmiterm([5 1 4 N1],B2,1);
lmiterm([5 1 6 0],(C2’+C2′)*Q^0.5);
lmiterm([5 1 7 P],1,Ad2);
lmiterm([5 1 7 P],1,Ad2);
lmiterm([5 2 2 Pr],Ar’,2,’s’);
lmiterm([5 2 2 S22],2/(1-beta),1);
lmiterm([5 2 5 Pr],2,1);
lmiterm([5 2 6 0],-2*Cr’*Q^0.5);
lmiterm([5 3 3 0],-2*(gama^2));
lmiterm([5 4 4 0],-2*(gama^2));
lmiterm([5 4 6 0],2*(Q^0.5));
lmiterm([5 5 5 0],-2*(gama^2));
lmiterm([5 6 6 0],-2);
lmiterm([5 7 7 S11],-2,1);
lmiterm([5 7 8 S12],-2,1);
lmiterm([5 8 8 S22],-2,1);
lmiterm([6 1 1 P],-1,1);
lmiterm([7 1 1 Pr],-1,1);
lmiterm([8 1 1 S],-1,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
mylmi1=getlmis;
[tmin,xfeasp]=feasp(mylmi1);
tmin
P=dec2mat(mylmi1,xfeasp,P);
Pr=dec2mat(mylmi1,xfeasp,Pr);
S=dec2mat(mylmi1,xfeasp,S);
N1=dec2mat(mylmi1,xfeasp,N1);
N2=dec2mat(mylmi1,xfeasp,N2);
M=P(1,1)+P(1,2);
K1=inv(M)*N1
K2=inv(M)*N2
سیستم طراحی شده در محیط Simulink برای مثال 5-1
شکل (A-2): سیستم طراحی شده در محیط Simulink برای مثال 5-1
M فایل مثال6-1
%%%%%%%%First M-file%%%%%%%%%%%
A1=[1 0.4;.2 -2];
B1=[1 ; 1];
C1=[1 0];
A2=[1.4 .4;.6 -2.5];
B2=[1.2 ; 1.2];
C2=[1 0];
Ad2=[.6 .9;-.1 0];
Ad1=[.3 .5;-.3 0];
%%%%%%%%%%%%%%%%%%%%%%%%%
D11=1*[1 ; 1];
D12=D11;
E11=1*[0.5 0];
Ed11=1*[0.5 0];
E12=E11;
Ed12=Ed11;
Ar=-1;
Cr=1;
beta=0.5;
Q=1;
Gamma=(2.15^2);
setlmis([]);
N1=lmivar(1,[1 1]);
N2=lmivar(1,[1 1]);
[P11,n,sP11]=lmivar(1,[1 1]);
[P12,n,sP12]=lmivar(2,[1 1]);
[P,n,sP]=lmivar(3,[sP11,sP12;sP12′,sP11]);
Pr=lmivar(1,[1 1]);
[S11,n,sS11]=lmivar(1,[2 1]);
[S12,n,sS12]=lmivar(2,[2 1]);
[S22,n,sS22]=lmivar(1,[1 1]);
[S,n,sS]=lmivar(3,[sS11,sS12;sS12′,sS22]);
EP11=lmivar(1,[1 1]);
DP11=lmivar(1,[1 1]);
EP22=lmivar(1,[1 1]);
DP22=lmivar(1,[1 1]);
EP12=lmivar(1,[1 1]);
DP12=lmivar(1,[1 1]);
EP21=lmivar(1,[1 1]);
DP21=lmivar(1,[1 1]);
EP112=lmivar(1,[1 1]);
DP112=lmivar(1,[1 1]);
EP121=lmivar(1,[1 1]);
DP121=lmivar(1,[1 1]);
EP212=lmivar(1,[1 1]);
DP212=lmivar(1,[1 1]);
EP221=lmivar(1,[1 1]);
DP221=lmivar(1,[1 1]);
%%%%%%%%%%%%%%%%%%%%%%%%1%%%%%%%%%%%%%%%%
lmiterm([1 1 1 P],A1′,1,’s’);
lmiterm([1 1 1 N1],B1,C1,’s’);
lmiterm([1 1 1 S11],1/(1-beta),1);
lmiterm([1 1 2 N1],-B1,Cr);
lmiterm([1 1 2 S12],1/(1-beta),1);
lmiterm([1 2 2 Pr],Ar’,1,’s’);
lmiterm([1 2 2 S22],1/(1-beta),1);
lmiterm([1 1 3 P],1,1);
lmiterm([1 1 4 N1],B1,1);
lmiterm([1 2 5 Pr],1,1);
lmiterm([1 3 3 0],-Gamma);
lmiterm([1 4 4 0],-Gamma);
lmiterm([1 5 5 0],-Gamma);
lmiterm([1 1 6 0],C1’*Q);
lmiterm([1 2 6 0],-Cr’*Q);
lmiterm([1 4 6 0],Q);
lmiterm([1 6 6 0],-1);
lmiterm([1 1 7 P],Ad1,1);
lmiterm([1 7 7 S11],-1,1);
lmiterm([1 7 8 S12],-1,1);
lmiterm([1 8 8 S22],-1,1);
lmiterm([1 1 9 P],1,D11);
lmiterm([1 1 10 0],E11′);
lmiterm([1 3 10 0],Ed11′);
lmiterm([1 9 9 EP11],-1,1);
lmiterm([1 10 10 DP11],-1,1);
%%%%%%%%%%%%%%%%%%%%%%%%2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
lmiterm([2 1 1 P],A2′,1,’s’);
lmiterm([2 1 1 N2],B2,C2,’s’);
lmiterm([2 1 1 S11],1/(1-beta),1);
lmiterm([2 1 2 N2],-B2,Cr);
lmiterm([2 2 2 Pr],Ar’,1,’s’);
lmiterm([2 1 2 S12],1/(1-beta),1);
lmiterm([2 2 2 S22],1/(1-beta),1);
lmiterm([2 1 3 P],1,1);
lmiterm([2 1 4 N2],B2,1);
lmiterm([2 2 5 Pr],1,1);
lmiterm([2 3 3 0],-Gamma);
lmiterm([2 4 4 0],-Gamma);
lmiterm([2 5 5 0],-Gamma);
lmiterm([2 1 6 0],C2’*Q);
lmiterm([2 2 6 0],-Cr’*Q);
lmiterm([2 4 6 0],Q);
lmiterm([2 6 6 0],-1);
lmiterm([2 1 7 P],Ad2,1);
lmiterm([2 7 7 S11],-1,1);
lmiterm([2 7 8 S12],-1,1);
lmiterm([2 8 8 S22],-1,1);
lmiterm([2 1 9 P],1,D11);
lmiterm([2 1 10 0],E11′);
lmiterm([2 3 10 0],Ed11′);
lmiterm([2 9 9 EP22],-1,1);
lmiterm([2 10 10 DP22],-1,1);
%%%%%%%%%%%%%%%%%%%%%%%%%1-2,2-1%%%%%%%%%%%%%%%%%%%%%%
lmiterm([3 1 1 P],A1′,1,’s’);
lmiterm([3 1 1 N2],B1,C2,’s’);
lmiterm([3 1 2 N2],-B1,Cr);
lmiterm([3 1 1 P],A2′,1,’s’);
lmiterm([3 1 1 N1],B2,C1,’s’);
lmiterm([3 1 2 N1],-B2,Cr);
lmiterm([3 1 1 S11],2/(1-beta),1);
lmiterm([3 1 2 S12],2/(1-beta),1);
lmiterm([3 2 2 S22],2/(1-beta),1);
lmiterm([3 2 2 Pr],Ar’,2,’s’);
lmiterm([3 1 3 P],2,1);
lmiterm([3 1 4 N2],B1,1);
lmiterm([3 1 4 N1],B2,1);
lmiterm([3 2 5 Pr],2,1);
lmiterm([3 3 3 0],-2*Gamma);
lmiterm([3 4 4 0],-2*Gamma);
lmiterm([3 5 5 0],-2*Gamma);
lmiterm([3 1 6 0],(C1+C2)’*Q);
lmiterm([3 2 6 0],-2*Cr’*Q);
lmiterm([3 4 6 0],2*Q);
lmiterm([3 6 6 0],-2);
lmiterm([3 1 7 P],(Ad1+Ad2),1);
lmiterm([3 7 7 S11],-2,1);
lmiterm([3 7 8 S12],-2,1);
lmiterm([3 8 8 S22],-2,1);
lmiterm([3 1 9 P],1,(D11+D12));
lmiterm([3 1 10 0],(E11’+E12′));
lmiterm([3 3 10 0],(Ed11’+Ed12′));
lmiterm([3 9 9 EP12],-1,1);
lmiterm([3 9 9 EP21],-1,1);
lmiterm([3 10 10 DP12],-1,1);
lmiterm([3 10 10 DP21],-1,1);
%%%%%%%%%%%%%%%%%%%1-1-2,1-2-1%%%%%%%%%%%%
lmiterm([4 1 1 P],A1′,1,’s’);
lmiterm([4 1 1 N1],B1,C2,’s’);
lmiterm([4 1 2 N1],-B1,Cr);
lmiterm([4 1 1 P],A1′,1,’s’);
lmiterm([4 1 1 N2],B1,C1,’s’);
lmiterm([4 1 2 N2],-B1,Cr);
lmiterm([4 1 1 S11],2/(1-beta),1);
lmiterm([4 1 2 S12],2/(1-beta),1);
lmiterm([4 2 2 S22],2/(1-beta),1);
lmiterm([4 2 2 Pr],Ar’,2,’s’);
lmiterm([4 1 3 P],2,1);
lmiterm([4 1 4 N1],B1,1);
lmiterm([4 1 4 N2],B1,1);
lmiterm([4 2 5 Pr],2,1);
lmiterm([4 3 3 0],-2*Gamma);
lmiterm([4 4 4 0],-2*Gamma);
lmiterm([4 5 5 0],-2*Gamma);
lmiterm([4 1 6 0],(C1+C1)’*Q);
lmiterm([4 2 6 0],-2*Cr’*Q);
lmiterm([4 4 6 0],2*Q);
lmiterm([4 6 6 0],-2);
lmiterm([4 1 7 P],(Ad1+Ad1),1);
lmiterm([4 7 7 S11],-2,1);
lmiterm([4 7 8 S12],-2,1);
lmiterm([4 8 8 S22],-2,1);
lmiterm([4 1 9 P],1,(D11+D11));
lmiterm([4 1 10 0],(E11’+E11′));
lmiterm([4 3 10 0],(Ed11’+Ed11′));
lmiterm([4 9 9 EP112],-1,1);
lmiterm([4 9 9 EP121],-1,1);
lmiterm([4 10 10 DP112],-1,1);
lmiterm([4 10 10 DP121],-1,1);
%%%%%%%%%%%%%%%%%%%%%%%2-1-2&2-2-1%%%%%%%%%%%%%%%%%%%%
lmiterm([5 1 1 P],A2′,1,’s’);
lmiterm([5 1 1 N1],B2,C2,’s’);
lmiterm([5 1 2 N1],-B2,Cr);
lmiterm([5 1 1 P],A2′,1,’s’);
lmiterm([5 1 1 N2],B2,C1,’s’);
lmiterm([5 1 2 N2],-B2,Cr);
lmiterm([5 1 1 S11],2/(1-beta),1);
lmiterm([5 1 2 S12],2/(1-beta),1);
lmiterm([5 2 2 S22],2/(1-beta),1);
lmiterm([5 2 2 Pr],Ar’,2,’s’);
lmiterm([5 1 3 P],2,1);
lmiterm([5 1 4 N1],B2,1);
lmiterm([5 1 4 N2],B2,1);
lmiterm([5 2 5 Pr],2,1);
lmiterm([5 3 3 0],-2*Gamma);
lmiterm([5 4 4 0],-2*Gamma);
lmiterm([5 5 5 0],-2*Gamma);
lmiterm([5 1 6 0],(C2+C2)’*Q);
lmiterm([5 2 6 0],-2*Cr’*Q);
lmiterm([5 4 6 0],2*Q);
lmiterm([5 6 6 0],-2);
lmiterm([5 1 7 P],(Ad2+Ad2),1);
lmiterm([5 7 7 S11],-2,1);
lmiterm([5 7 8 S12],-2,1);
lmiterm([5 8 8 S22],-2,1);
lmiterm([5 1 9 P],1,(D12+D12));
lmiterm([5 1 10 0],(E12’+E12′));
lmiterm([5 3 10 0],(Ed12’+Ed12′));
lmiterm([5 9 9 EP212],-1,1);
lmiterm([5 9 9 EP221],-1,1);
lmiterm([5 10 10 DP212],-1,1);
lmiterm([5 10 10 DP221],-1,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
lmiterm([15 1 1 P],-1,1);
lmiterm([16 1 1 Pr],-1,1);
lmiterm([17 1 1 S],-1,1);
lmiterm([18 1 1 EP11],-1,1);
lmiterm([19 1 1 EP12],-1,1);
lmiterm([20 1 1 EP21],-1,1);
lmiterm([21 1 1 EP22],-1,1);
lmiterm([22 1 1 DP11],-1,1);
lmiterm([23 1 1 DP12],-1,1);
lmiterm([24 1 1 DP21],-1,1);
lmiterm([25 1 1 DP22],-1,1);
lmiterm([26 1 1 EP112],-1,1);
lmiterm([27 1 1 EP121],-1,1);
lmiterm([28 1 1 EP212],-1,1);
lmiterm([29 1 1 EP221],-1,1);
lmiterm([30 1 1 DP112],-1,1);
lmiterm([31 1 1 DP121],-1,1);
lmiterm([32 1 1

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