A=rand(4)

A =

    0.9501    0.8913    0.8214    0.9218
    0.2311    0.7621    0.4447    0.7382
    0.6068    0.4565    0.6154    0.1763
    0.4860    0.0185    0.7919    0.4057

eig(A)

ans =

   2.3230          
   0.0914 + 0.4586i
   0.0914 - 0.4586i
   0.2275          

A=A-3*eye(4)

A =

   -2.0499    0.8913    0.8214    0.9218
    0.2311   -2.2379    0.4447    0.7382
    0.6068    0.4565   -2.3846    0.1763
    0.4860    0.0185    0.7919   -2.5943

lmis=set([ ])
empty SET
P=sdpvar(4)
Linear matrix variable 4x4 (symmetric, real, 10 variables)
lmis=lmis+set(P>0)
+++++++++++++++++++++++++++++++++++++++++++++++++
|   ID|      Constraint|                    Type|
+++++++++++++++++++++++++++++++++++++++++++++++++
|   #1|   Numeric value|   Matrix inequality 4x4|
+++++++++++++++++++++++++++++++++++++++++++++++++
lmis=lmis+set(A'*P+P*A+eye(4)<0)
+++++++++++++++++++++++++++++++++++++++++++++++++
|   ID|      Constraint|                    Type|
+++++++++++++++++++++++++++++++++++++++++++++++++
|   #1|   Numeric value|   Matrix inequality 4x4|
|   #2|   Numeric value|   Matrix inequality 4x4|
+++++++++++++++++++++++++++++++++++++++++++++++++
sol=solvesdp(lmis,trace(P))
SeDuMi 1.1R3 by AdvOL, 2006 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, theta = 0.250, beta = 0.500
eqs m = 10, order n = 9, dim = 33, blocks = 3
nnz(A) = 68 + 0, nnz(ADA) = 100, nnz(L) = 55
 it :     b*y       gap    delta  rate   t/tP*  t/tD*   feas cg cg  prec
  0 :            5.74E+00 0.000
  1 :  -1.35E+00 1.90E+00 0.000 0.3310 0.9000 0.9000   2.23  1  1  2.5E+00
  2 :  -1.31E+00 5.93E-01 0.000 0.3122 0.9000 0.9000   2.38  1  1  4.6E-01
  3 :  -1.30E+00 2.48E-02 0.000 0.0418 0.9900 0.9900   1.41  1  1  1.6E-02
  4 :  -1.30E+00 2.22E-06 0.354 0.0001 1.0000 1.0000   1.01  1  1  1.4E-06
  5 :  -1.30E+00 6.19E-09 0.195 0.0028 0.9990 0.9990   1.00  1  1  4.0E-09
  6 :  -1.30E+00 1.30E-11 0.000 0.0021 0.9990 0.9990   1.00  1  1  8.3E-12

iter seconds digits       c*x               b*y
  6      0.2   Inf -1.3044668936e+00 -1.3044668936e+00
|Ax-b| =   1.3e-11, [Ay-c]_+ =   1.6E-12, |x|=  8.4e-01, |y|=  7.5e-01

Detailed timing (sec)
   Pre          IPM          Post
1.400E-01    1.900E-01    5.000E-02    
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.10477.

sol = 

    yalmiptime: 0.6760
    solvertime: 0.4782
          info: 'No problems detected (SeDuMi-1.1)'
       problem: 0
        dimacs: [6.7491e-12 0 0 8.0046e-13 -7.1974e-13 7.6965e-13]

Plmi=double(P)

Plmi =

    0.3501    0.1442    0.1790    0.1559
    0.1442    0.3118    0.1465    0.1246
    0.1790    0.1465    0.3488    0.1508
    0.1559    0.1246    0.1508    0.2938

PLyap=lyap(A',eye(4))

PLyap =

    0.3501    0.1442    0.1790    0.1559
    0.1442    0.3118    0.1465    0.1246
    0.1790    0.1465    0.3488    0.1508
    0.1559    0.1246    0.1508    0.2938

abs(Plmi-PLyap)

ans =

   1.0e-11 *

    0.0204    0.1156    0.0135    0.0643
    0.1156    0.1727    0.0603    0.0654
    0.0135    0.0603    0.0367    0.0303
    0.0643    0.0654    0.0303    0.0717

checkset(lmis)
 
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|   ID|      Constraint|                Type|   Primal residual|   Dual residual|
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|   #1|   Numeric value|   Matrix inequality|           0.16328|      7.7447e-14|
|   #2|   Numeric value|   Matrix inequality|       -1.6009e-12|          0.1634|
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++