实例2"/>
LMI实例2
%1.定义线性矩阵不等式约束
setlmis([]);
A=[-1 -2 1;3 2 1;1 -2 -1];
B=[1;0;1];
Q=[1 -1 0;-1 -3 -12;0 -12 -36];
X=lmivar(1,[3 1]); % 变量X,满对称的
lmiterm([1 1 1 X],1,A,'s');
lmiterm([1 1 1 0],Q);
lmiterm([1 2 2 0],-1);
lmiterm([1 2 1 X],B',1);
LMIs=getlmis;
c=mat2dec(LMIs,eye(3));%将目标函数写成,其中)(TraceXxcTx是矩阵变量X中的独立元所构成的向量。%由于引进向量的目的是要选择cX的对角元,因此它可以作为相应于IX=的决策向量得到,即
options=[1e-5,0,0,0,0];
>> [copt,xopt]=mincx(LMIs,c,options);%调用mincx计算最小值xopt,目标函数的全局最小值copt=c’*xopt,%其中1e-5给定了所要求的关于copt的计算精度。作为求解器mincx运行的结果,以下的信息将出现在屏幕上Solver for linear objective minimization under LMI constraints Iterations : Best objective value so far 12 -8.5114763 -13.063640
*** new lower bound: -34.0239784 -15.768450
*** new lower bound: -25.0056045 -17.123012
*** new lower bound: -21.3067816 -17.882558
*** new lower bound: -19.8194717 -18.339853
*** new lower bound: -19.1894178 -18.552558
*** new lower bound: -18.9196689 -18.646811
*** new lower bound: -18.80370810 -18.687324
*** new lower bound: -18.75390311 -18.705715
*** new lower bound: -18.73257412 -18.712175
*** new lower bound: -18.72349113 -18.714880
*** new lower bound: -18.71962414 -18.716094
*** new lower bound: -18.71798615 -18.716509
*** new lower bound: -18.71729716 -18.716695
*** new lower bound: -18.716873Result: feasible solution of required accuracybest objective value: -18.716695guaranteed relative accuracy: 9.50e-06f-radius saturation: 0.000% of R = 1.00e+09
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LMI实例2
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