Re: numerical problem state feedback delay lmi

[Johan Löfberg]

No particular reason, except perhaps the fact that the optimal Y is very large in absolute sense (on the order of 10^4-10^5 when I use sdpt3 and mosek). SDPT3 and Mosek solves the problem without any announced numerical problems

[Johan Löfberg]

BTW, to prepare your code for the case p=n, you should write

Y{i}=sdpvar(p,n,'full');

[djamel Cher]

thank you for replying 

even if i used spdt3 or LMILAB  and the problem is solved still , i dont get the stability requirement (insability)?

 

another question, if the problem is solved by any arbitrary solver does it mean that my work or theory is right ?

thank in advance

[Johan Löfberg]

I have no idea what you are saying.

When I solve it using Mosek, SDPT3 or SeDuMi, they all return strictly feasible solution, and they all display nice gap statistics etc.

>> checkset(Cont2)
 
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|   ID|          Constraint|   Primal residual|   Dual residual|
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|   #1|   Matrix inequality|        7.4998e-08|      6.7215e-14|
|   #2|   Matrix inequality|        7.5115e-08|      4.2269e-13|
|   #3|   Matrix inequality|        1.5011e-07|      5.5147e-14|
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

[djamel Cher]

if the problem is solved by any arbitrary solver does it mean that my work or theory is right ? 

when i implement the values obtained in simulink or in the model i get divergence (instability) aven if the lmi is solved 

thank you again johan

[Johan Löfberg]

The solvers find a solution to the LMI.

Whether your theory is correct or not is impossible for us to answer. If your theory says that a solution of this LMI proves stability, but simulations shows instability, then your theory is wrong, your simulation is wrong, or you have implemented the LMI incorrectly.

[djamel Cher]

hi johan 

I still wonder , if the partical or numerical example (model)  used in the theory and the descretisation process (like euler) can generate such problem (lmi instability)

[Johan Löfberg]

All discretization schemes have stability limitations according to standard numerical analysis.

An LMI can not be unstable, so I don't know what you mean with that