按照公式写的LMi不能求解，解出来的全部都是NaN;

如果论文中求解出的值gamma1=0.267;gamma2=0.2281;gamma3=1.8e-4;beta=3.99;但还是出现  info: 'Infeasible problem (SDPT3-4)'

求大佬帮忙看一下是我写的LMI中的F和solvesdp有错；还是需要yalmip其他的工具才能解LMI(我用的是sdpt3)

程序：

clc

clear all

close all

A=[-0.439 0;

1 -4.195];

Bu=[0.002864;0];

C=[0 1];

% A=[-4.6340 -1.8416;

%     1.0 0];

Bu=[1;0];

C=[0 0.002864];

Bf=[0;0];

Bd=[0.2;0.5];

Dd=0.1;

Df=1;

lambda1=4;

lambda2=2;

lambda3=2;

rho1=1;

rho2=1;

rho3=1;

rho4=1;

theta=0.05;

gamma1=0.267;

gamma2=0.2281;

gamma3=1.8e-4;

beta=3.99;

% gamma1=sdpvar(1);

% gamma2=sdpvar(1);

% gamma3=sdpvar(1);

% beta=sdpvar(1);

M1=sdpvar(1,2,'full');%,'full'

M2=sdpvar(2,1,'full');

X1=sdpvar(2,2,'full');

X2=sdpvar(2,2,'full');

Xhat2=sdpvar(1);

P11=sdpvar(4,4,'symmetric');

P12=sdpvar(4,4,'symmetric');

P13=sdpvar(4,4,'symmetric');

P21=sdpvar(4,4,'symmetric');

P22=sdpvar(4,4,'symmetric');

P23=sdpvar(4,4,'symmetric');

P31=sdpvar(4,4,'symmetric');

P32=sdpvar(4,4,'symmetric');

P33=sdpvar(4,4,'symmetric');

P41=sdpvar(4,4,'symmetric');

P42=sdpvar(4,4,'symmetric');

P43=sdpvar(4,4,'symmetric');

%%%%%%%%%%%%%%%%%%%%

Pi1=[A'*X1-lambda1*C'*M2'  -M1'*Bu';

zeros(2)                        A'*X2+M1'*Bu'];

Pi2=[A'*X1-lambda2*C'*M2'  -M1'*Bu';

zeros(2)                        A'*X2+M1'*Bu'];

Pi3=[A'*X1-lambda3*C'*M2'  -M1'*Bu';

zeros(2)                        A'*X2+M1'*Bu'];

X=[X1 zeros(2);

zeros(2) X2];

Psi1=[X1'*Bd-lambda1*M2*Dd;

X2'*Bd];

Psi2=[X1'*Bd-lambda2*M2*Dd;

X2'*Bd];

Psi3=[X1'*Bd-lambda3*M2*Dd;

X2'*Bd];

Phi1=[X1'*Bf-lambda1*M2*Df;

X2'*Bf];

Phi2=[X1'*Bf-lambda2*M2*Df;

X2'*Bf];

Phi3=[X1'*Bf-lambda3*M2*Df;

X2'*Bf];

Xi11=lambda1^2*[C zeros(1,2)]'*[C zeros(1,2)];

Xi12=lambda2^2*[C zeros(1,2)]'*[C zeros(1,2)];

Xi13=lambda3^2*[C zeros(1,2)]'*[C zeros(1,2)];

Xi31=lambda1^2*[C zeros(1,2)]';

Xi32=lambda2^2*[C zeros(1,2)]';

Xi33=lambda3^2*[C zeros(1,2)]';

Xi4=[zeros(2,2) eye(2)]'*[zeros(2,2) eye(2)];

Xi2_11=P11+theta*Pi1-X';

Xi2_21=P21+theta*Pi1-X';

Xi2_31=P31+theta*Pi1-X';

Xi2_41=P41+theta*Pi1-X';

Xi2_12=P12+theta*Pi2-X';

Xi2_22=P22+theta*Pi2-X';

Xi2_32=P32+theta*Pi2-X';

Xi2_42=P42+theta*Pi2-X';

Xi2_13=P13+theta*Pi3-X';

Xi2_23=P23+theta*Pi3-X';

Xi2_33=P33+theta*Pi3-X';

Xi2_43=P43+theta*Pi3-X';

%%%%%%%%%%%LMI

Lmi11=[Pi1+Pi1'+Xi11   Xi2_11    Psi1+Xi31*Dd;

(Xi2_11)'  -theta*(X+X')  theta*Psi1;

(Psi1+Xi31*Dd)' (theta*Psi1)' lambda1^2*Dd'*Dd-gamma1^2*eye(1)];

Lmi12=[Pi2+Pi2'+Xi12   Xi2_12    Psi2+Xi32*Dd;

(Xi2_12)'  -theta*(X+X')  theta*Psi2;

(Psi2+Xi32*Dd)' (theta*Psi2)' lambda2^2*Dd'*Dd-gamma1^2*eye(1)];

Lmi13=[Pi3+Pi3'+Xi13   Xi2_13    Psi3+Xi33*Dd;

(Xi2_13)'  -theta*(X+X')  theta*Psi3;

(Psi3+Xi33*Dd)' (theta*Psi3)' lambda3^2*Dd'*Dd-gamma1^2*eye(1)];

Lmi21=[Pi1+Pi1'-Xi11   Xi2_21    Phi1-Xi31*Df;

(Xi2_21)'  -theta*(X+X')  theta*Phi1;

(Phi1-Xi31*Df)' (theta*Phi1)' -lambda1^2*Df'*Df+beta^2*eye(1)];

Lmi22=[Pi2+Pi2'-Xi12   Xi2_22    Phi2-Xi32*Df;

(Xi2_22)'  -theta*(X+X')  theta*Phi2;

(Phi2-Xi32*Df)' (theta*Phi2)' -lambda2^2*Df'*Df+beta^2*eye(1)];

Lmi23=[Pi3+Pi3'-Xi13   Xi2_23    Phi3-Xi33*Df;

(Xi2_23)'  -theta*(X+X')  theta*Phi3;

(Phi3-Xi33*Df)' (theta*Phi3)' -lambda3^2*Df'*Df+beta^2*eye(1)];

Lmi31=[Pi1+Pi1'+Xi4   Xi2_31    Psi1;

(Xi2_31)'  -theta*(X+X')  theta*Psi1;

(Psi1)' (theta*Psi1)' -gamma2^2*eye(1)];

Lmi32=[Pi2+Pi2'+Xi4   Xi2_32    Psi2;

(Xi2_32)'  -theta*(X+X')  theta*Psi2;

(Psi2)' (theta*Psi2)' -gamma2^2*eye(1)];

Lmi33=[Pi3+Pi3'+Xi4   Xi2_33    Psi3;

(Xi2_33)'  -theta*(X+X')  theta*Psi3;

(Psi3)' (theta*Psi3)' -gamma2^2*eye(1)];

Lmi41=[Pi1+Pi1'+Xi4   Xi2_41    Phi1;

(Xi2_41)'  -theta*(X+X')  theta*Phi1;

(Phi1)' (theta*Phi1)' -gamma3^2*eye(1)];

Lmi42=[Pi2+Pi2'+Xi4   Xi2_42    Phi2;

(Xi2_42)'  -theta*(X+X')  theta*Phi2;

(Phi2)' (theta*Phi2)' -gamma3^2*eye(1)];

Lmi43=[Pi3+Pi3'+Xi4   Xi2_43    Phi3;

(Xi2_43)'  -theta*(X+X')  theta*Phi3;

(Phi3)' (theta*Phi3)' -gamma3^2*eye(1)];

F=[gamma3>=0,gamma1>=0,gamma2>=0,beta>=0;

P11>=0,P12>=0,P13>=0;

P21>=0,P22>=0,P23>=0;

P31>=0,P32>=0,P33>=0;

P41>=0,P42>=0,P43>=0;

Lmi11<=0,Lmi12<=0,Lmi13<=0;

Lmi21<=0,Lmi22<=0,Lmi23<=0;

Lmi31<=0,Lmi32<=0,Lmi33<=0;

Lmi41<=0,Lmi42<=0,Lmi43<=0;

];

F2=[Bu'*X2==Xhat2*Bu';F];

h=rho1*gamma1+rho2*gamma2+rho3*gamma3-rho4*beta;

solvesdp(F2,h)

gamma1=double(gamma1);

gamma2=value(gamma2);

gamma3=value(gamma3);

beta=value(beta);

X1=value(X1)

X2=value(X2);

Xhat2=value(Xhat2)

M1=value(M1);

M2=value(M2);

F1=(M2'*inv(X1))'

K=(M1'*inv(Xhat2))'

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