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1 | clc |
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2 | echo on |
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3 | %********************************************************* |
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4 | % |
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5 | % Decay-rate estimation using non-convex SDP |
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6 | % |
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7 | %********************************************************* |
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8 | % |
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9 | % The problem we solve is estimatation of decay-rate of a |
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10 | % linear system x' = Ax. This can be formulated as a |
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11 | % generalized eigenvalue problem (GEVP) |
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12 | % |
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13 | % max alpha |
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14 | % s.t A'P+PA < -2alphaP |
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15 | % P > I |
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16 | % |
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17 | % This time, we solve it as a BMI using PENBMI (hence you |
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18 | % need PENBMI to run this demo). Note, this is a quasi-convex |
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19 | % problem, and PENBMI is actually guaranteed to find the |
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20 | % global optima. |
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21 | pause |
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22 | clc |
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23 | |
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24 | % Define the variables |
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25 | A = [-1 2;-3 -4]; |
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26 | P = sdpvar(2,2); |
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27 | alpha = sdpvar(1,1); |
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28 | pause |
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29 | |
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30 | % Define the GEVP |
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31 | F = set(P>eye(2))+set(A'*P+P*A < -2*alpha*P) + set(alpha > 0); |
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32 | pause |
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33 | % Maximize alpha (minimize -alpha) |
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34 | solvesdp(F,-alpha); |
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35 | double(alpha) |
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36 | pause |
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