Uncontrollable States in State Space

[Eidos]

Hi Guys/Gals

If you end up with a row of zeros in the controllability matrix for a linear state space system, does that row correspond with the state that is uncontrollable


eg. Assuming a linear state space system with 5 states, a row of zeros in the 4th row of the controllability matrix corresponds to the 4th state of the system being uncontrollable.

Secondly, if we have a repeated row in the controllability matrix what does that imply?

Thanks

 

[trambolin]

The controllability matrix does not tell you which state is uncontrollable. A row of zeros or in general, controllability matrix which does not have full rank indicates the existence of an uncontrollable part of your system.

You can transform your system with a Kalman controllable/uncontrollable decomposition and see which states are uncontrollable.