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ÇóÖú~ÓдóÉñ¿ÉÒÔ°ïæ¿´Ò»Ï³ÌÐòÂ𣿠³°ô¿ØÖÆ+ʱÖÍÎÊÌ⣬Ï븴ÏÖÒ»ÏÂÎÄÕµÄÀý×Ó2. Õâ¸ölmi³ÌÐòÔÚmatlabÀï¿ÉÒÔÇó½â£¬tmin<0£¬ÓÐÖµ£¬µ«Êǵõ½µÄ½á¹û²»¶Ô£¬µÃµ½µÄ·´À¡ÂÉK½Ó½ü0£¬¸úÎÄÖеÄËãÀýµÄ½á¹û²»Ò»Ñù£¬²»ÖªµÀÊÇÄÄÀï´íÁË£¬¿ÉÒÔÓÐÈ˰ïæ½â¾öÒ»ÏÂÂ𣿶àлÁË~ %% 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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