Trying to formulate and solve a LMI

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Ashik Rahman 2021-12-18

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评论： Ashik Rahman 2021-12-21

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I am very new to LMI and trying to solve the following LMI

((I + UC)A)'P + P(I + UC)A

+ (VCA)'Y' + Y(VCA)

-C'K' -KC< 0

and P>0

I have formulated the code below following https://www.mathworks.com/help/robust/ref/lmiterm.html

Am I doing it correct? geting a warning Warning: In (1,1) block of LMI #1, non-symmetric term AXB was replaced by (AXB+B'XA')/2. For safety, set FLAG='s' to specify AXB+B'XA' in one shot.

and following message

These LMI constraints were found infeasible

Thank you in advance

    CD_Plus = inv((C*D)'*(C*D))*(C*D)';
    U = -D*CD_Plus;
    V1 = (C*D)*CD_Plus;
    V = eye(length(V1))-((C*D)*CD_Plus);
    %% LMI
    Q = (eye(size(U*C,1))+U*C)*A;
    M = V*C*A;
    C1(1,:) =C;
    
    setlmis([]);
    P = lmivar(1,[size(Q,1) 1]);
    K1 = lmivar(1,[size(C1,1) 1]);
    Y1 = lmivar(1,[size(M,2) 1]);
    
    lmiterm([-1 1 1 P],1,1); % P>0
    lmiterm([1 1 1 P],1,(eye(size(U*C,1))+U*C)*A,'s'); % ((I+UC)*A)'*P+P*(I+UC)*A
    lmiterm([1 1 2 Y1],1,V*C*A); % Y*(V*C*A)
    lmiterm([1 1 2 -Y1],(V*C*A)',1); % (V*C*A)'Y'
    lmiterm([1 2 1 0],-1);
    lmiterm([1 2 2 0],1);
    lmiterm([-1 1 1 K1],1,C1); % K*C
    lmiterm([-1 1 1 -K1],C1',1); % C'*K'
    
    LMISYS = getlmis;
    [tmin,XFEAS]=feasp(LMISYS);
    P=dec2mat(LMISYS,XFEAS,P);
    K1=dec2mat(LMISYS,XFEAS,K1);
 