LMI feasible whatever the T parameter??

[elmajidi azeddine]

Hello Professor,

In order to get familiar with delayed nonlinear, i picked up a delayed LTI system example cited in various paper, in which it is said that the latter system is stable till a given value of T (best case T=4.472), however whatever the value i give to T, it got me always feasible!!!, in addition when i perform the simulation it is clear that system beyond T=5 got instable. I'm not sure what i did wrong in my LMIs.

Another question, if i get from the solver that the primal and the dual problem is feasible and in the same time i got a negative eigenvalue from one of my matrix variable (which should be definite positive), what should i understand?

Could you please help?

Thank you in advance.

[Johan Löfberg]

This

issymmetric(Pfeasible)

is a completely redundant check. It cannot be unsymmetric as it is structurally symmetric

Your model is not well posed as it is homogenuous, thus 0 is always feasible

>> assign(P,0);assign(Q,0);assign(X,0);assign(W,0);assign(Y,0);

>> check(Constraints)

 

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

|   ID|          Constraint|   Primal residual|   Dual residual|

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

|   #1|   Matrix inequality|                 0|             NaN|

|   #2|   Matrix inequality|                 0|             NaN|

|   #3|   Matrix inequality|                 0|             NaN|

|   #4|   Matrix inequality|                 0|             NaN|

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

some constraint must be intended to be a strict inequality. Using P >= I leads to infeasibility

[Johan Löfberg]

https://yalmip.github.io/faq/solutionviolated/