How To solve a LMI(Linear Matrix Inequalitiy)?

Question

Farid 2015-4-18

0
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https://ww2.mathworks.cn/matlabcentral/answers/210259-how-to-solve-a-lmi-linear-matrix-inequalitiy

评论： ayman halabi 2018-12-5

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We have a satate-space system like:

X^=A*X+B_w*W+B_u*U+B_ref*V_ref Y=C_y*X+C_yw*W+D_yu*U

Where:

A=

[  0     -1612.9      0
    833.3    -34.7       0
      0       -1         0]

B_w=

    [    0
     -1666.7
         0  ]

B_u=

    [46452
     -1000
        0 ]

B_ref=

      [0
       0
       1]

C_y=[0 1 0]

D_yw=[0]

D_yu=[0]

And there are constraints as:

LMI1:

           [A*W+W*A’+B_u*Y+Y’*B_u’     B_w      W*C_y’+Y’*D_yu’
                     B_w’             -2.89           0
                C_y*W+D_yu*Y            0           -2.89      ] < 0

LMI2:

A*W+W*A’+B_u*Y+Y’*B_u’+260*W < 0

LMI3:

           [-125660*W    W*A’+Y’*B_u’
            A*W+B_u*Y     -125660*W ] < 0

LMI4:

     [ 0.906(A*W+W*A’+B_u*Y+Y’*B_u’)            0.423(A*W-W*A’+B_u*Y-Y’*B_u’)
      -0.423(A*W-W*A’+B_u*Y-Y’*B_u’)            0.906(A*W+W*A’+B_u*Y+Y’*B_u’)] < 0

Here, unknown matrices are Y and W that LMI should be solved to find them. I wonder if someone could help me with this. Besides, I need the code to solve other LMIs. Thanks.