How To solve a LMI(Linear Matrix Inequalitiy)?
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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.
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