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%% lmi Ô­ÎÄËãÀý 2009Theorem4
clear

E=[1 0; 0 0];
A=[0 0.46;-1 -2];
B1=[1 1.5]';
D=[0.2 0; 0 0.2];
D1=D;

H=eye(2);
H1=[1 1]';

[~,na]=size(A);
taomax0=1.5;

%% LMI¶¨Òå
setlmis([])
%¶¼ÊÇÈÎÒâ½×ÊýΪAµÄ¾ØÕó
Q1=lmivar(2,[na,na]);%ÊÇna*naµÄ·Ç¶Ô³ÆÕó
Z1=lmivar(2,[na,na]);
% Q1=lmivar(1,[na,1]);%ÊÇna*naµÄ¶Ô³ÆÕó
% Z1=lmivar(1,[na,1]);

N=lmivar(2,[1,na]);   %NµÄ½×Êý£¨x,y£©£¬xÊÇBµÄÁÐÊý£¬ÊÇuµÄ½×Êý,yÒѸüÕýΪna½×
X=lmivar(2,[na,na]);  %X·ÇÆæÒì
X1=lmivar(2,[na,na]);
Y1=lmivar(2,[na,na]);
eps0=lmivar(1,[1,0]); %¶¨Òå±êÁ¿µÄʱºò£¬ºóÃæÄǸöÓ¦¸ÃÊÇд0 µ«ÊÇд0д1¶¼²»Ó°Ïì
eps1=lmivar(1,[1,0]);

%% ²»µÈʽÃèÊö
%           
lmiterm([-1 1 1 Q1],1,1);
lmiterm([-2 1 1 Z1],1,1);

% 2nd LMI  
%sum11
lmiterm([3 1 1 X],A,1,'s');  
lmiterm([3 1 1 X1],taomax0,1);
lmiterm([3 1 1 Y1],1,1,'s');
lmiterm([3 1 1 Q1],1,1);
lmiterm([3 1 1 eps0],1,D*D');
lmiterm([3 1 1 eps1],1,D1*D1');

%sum12
lmiterm([3 1 2 N],B1,1);  
lmiterm([3 1 2 Y1],-1,1);  

%sum22
lmiterm([3 2 2 Q1],-1,1);

%(theta12)
lmiterm([3 1 3 -X],taomax0,A');
lmiterm([3 1 3 eps0],1,taomax0*(D*D'));
lmiterm([3 1 3 eps1],1,taomax0*(D1*D1'));
lmiterm([3 2 3 -N],taomax0,B1');

%(theta22)
lmiterm([3 3 3 Z1],-taomax0,1);  
lmiterm([3 3 3 eps0],1,taomax0*taomax0*(D*D'));
lmiterm([3 3 3 eps1],1,taomax0*taomax0*(D1*D1'));

%(theta13)
lmiterm([3 1 4 -X],1,H');
lmiterm([3 2 5 -N],1,H1');

%(theta33)
lmiterm([3 4 4 eps0],-eye(2),1);
lmiterm([3 5 5 eps1],-eye(2),1);

% lmiterm([3 4 4 eps0],-1,1);
% lmiterm([3 5 5 eps1],-1,1);

lmis=getlmis;
options(5)=1;
[tmin,feas]=feasp(lmis,options)

%% Çó½â¿ØÖƲÎÊý
N=dec2mat(lmis,feas,N)
X=dec2mat(lmis,feas,X)
Y1=dec2mat(lmis,feas,Y1)
X1=dec2mat(lmis,feas,X1)
Q1=dec2mat(lmis,feas,Q1)
Z1=dec2mat(lmis,feas,Z1)
eps0=dec2mat(lmis,feas,eps0)
eps1=dec2mat(lmis,feas,eps1)

K=N/X
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  • ¸½¼þ 1 : 2009.pdf
  • 2015-11-17 09:58:47, 444.21 K

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