The solver mosek showed " Successfully solved", but the results are all zeros , iterations:0.

[Green Jeff]

In the simulation, The solver mosek showed " Successfully solved", but the results are all zeros , iterations:0.

Other solves such as sedumi, sdpt3 also showed Successfully solved,but the results obviously are wrong,

The part eigenvalue of the constrained positive definite matrix is less than zero.

The related theories of linear matrix inequalities are derived from two references in the attachments.

How can I solve this problem?

[Johan Löfberg]

If you look at the display of your list of constraints, you can see that you haven't defined any semidefinite constraints, but a bunch of elementwise constraints. The reason is that your matrices are not symmetric

>> S

Linear matrix variable 27x27 (full, real, 139 variables)

Eigenvalues between [-7.8149,7.6497]

Coeffiecient range: 0.06 to 6.5

>> 

S being full (i.e. not symmetric) comes e.g. from S11 being full, which comes from using this expression in a diagonal block

-miu*V11+V11'

Linear matrix variable 4x4 (full, real, 12 variables)

Eigenvalues between [0,0]

Coeffiecient range: 1 to 1

btw, there is no command called solvesdp. it is obsolete syntax

[Green Jeff]

Thank you very much for your help. This problem has troubled me for more than a month. Now I finally have a solution. 

Once again, thank you for your help. I really appreciate it. Now I can finally see the dawn.