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1 | clc |
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2 | echo on |
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3 | yalmip('clear') |
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4 | %********************************************************* |
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5 | % |
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6 | % Modeling and solving KYP problems |
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7 | % |
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8 | %********************************************************* |
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9 | % |
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10 | % This example requires the KYPD-solver. |
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11 | % |
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12 | % We will show how we can use the dedicated |
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13 | % KYPD solver to solve a L2-gain analysis problem. |
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14 | % |
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15 | % minimize t |
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16 | % s.t [A'P+PA+C'C PB;B'P -t] < 0 |
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17 | % P > 0 |
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18 | % |
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19 | pause |
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20 | |
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21 | % Define a random stable system |
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22 | n = 30; |
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23 | A = randn(n);A = A - max(real(eig(A)))*eye(n)*1.5; |
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24 | B = randn(n,1); |
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25 | C = randn(1,n); |
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26 | pause |
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27 | |
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28 | % YALMIP variables |
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29 | t = sdpvar(1,1); |
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30 | P = sdpvar(n,n); |
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31 | pause |
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32 | |
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33 | % KYP constraint |
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34 | % NOTE : Do not add the constraint P>0 |
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35 | % if you want to use the KYPD solver) |
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36 | F = set(kyp(A,B,P,blkdiag(C'*C,-t)) < 0) |
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37 | pause |
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38 | |
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39 | % Solve using dedicated solver |
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40 | sol1 = solvesdp(F,t,sdpsettings('solver','kypd')); |
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41 | pause |
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42 | |
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43 | % Solve using SeDuMi (or any other standard SDP solver) |
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44 | sol2 = solvesdp(F,t,sdpsettings('solver','sedumi')); |
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45 | pause |
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46 | |
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47 | % Compare solution time (this can be a bit mis-leadinhg due to memory caching etc...) |
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48 | % KYPD should typically be a lot faster than the straight-forward solution |
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49 | sol1.solvertime/sol2.solvertime |
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50 | |
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51 | pause |
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52 | echo off |
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