Definition of observability indices?

[james1234]

If someone could please provide me with a simple explanation for observability indices I would be most grateful!

According to wikipedia;

"The Observability index (v) of a linear time-invariant discrete system is the smallest natural number for which is satisfied that rank(Ov) = rank(Ov + 1)"

Can anyone tell me what is meant by the "smallest natural number"? according to slide 8/11 of this link - http://support.dce.felk.cvut.cz/pub/roubalj/teaching/SpaceMaster/lectures/SSMI_Observability.pdf

the observability index would appear to be the maximum rank for a specific output vector (C)? yes?

many thanks!

Jamie

 

[Resonance]

"The Observability index (v) of a linear time-invariant discrete system is the smallest natural number for which is satisfied that rank(Ov) = rank(Ov + 1)"

Hi,
Sorry for my Englsih.
Did you hear about Kalman observability matrix? Ov - like Kalman observability matrix, but the highest power of the matrix Ov is v.