lyapunov.m

 システム
   
の安定解析問題に関する連立 LMI
   
を解く.
 なお,このシステムは安定である.

実行結果

>> lyapunov

SeDuMi 1.3 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, theta = 0.250, beta = 0.500
eqs m = 3, order n = 5, dim = 9, blocks = 3
nnz(A) = 9 + 0, nnz(ADA) = 9, nnz(L) = 6
 it :     b*y       gap    delta  rate   t/tP*  t/tD*   feas cg cg  prec
  0 :            2.89E+001 0.000
  1 :  0.00E+000 6.12E+000 0.000 0.2116 0.9000 0.9000   0.02  1  1  7.8E+000
  2 :  0.00E+000 2.17E-001 0.000 0.0355 0.9900 0.9900   0.43  1  1  3.4E-001
  3 :  0.00E+000 1.50E-005 0.000 0.0001 1.0000 1.0000   0.97  1  1  2.4E-005
  4 :  0.00E+000 1.51E-012 0.000 0.0000 1.0000 1.0000   1.00  1  1  2.4E-012

iter seconds digits       c*x               b*y
  4      0.1   1.5 -1.0737681173e-012  0.0000000000e+000
|Ax-b| =  1.0e-012, [Ay-c]_+ =  0.0E+000, |x|= 1.1e-012, |y|= 8.4e+000

Detailed timing (sec)
   Pre          IPM          Post
1.500E-002    5.000E-002    6.005E-003    
Max-norms: ||b||=0, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.18267.
sol = 
    yalmiptime: 0.1510
    solvertime: 0.0720
          info: 'No problems detected (SeDuMi-1.3)'
       problem: 0
        dimacs: [1.0438e-012 0 0 0 -1.0738e-012 2.8065e-012]
P_feas =
    7.9115    1.1877
    1.1877    2.4300
ans =
     1     1
ans =
     1     1
    
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