Number of poles and rank of controllability matrix

AI Thread Summary
The discussion revolves around a system with a transfer function indicating three poles and a controllability matrix rank of four. It concludes that the system must have at least four states. If the system is of fourth order, it is deemed controllable but not observable. However, if the system is of a higher order, the observability status remains uncertain. The key takeaway is that there are three observable modes and four controllable modes in this context.
lampus
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Hi!
I have a little problem. I have an exercise where it's said that the tranfer function gives 3 poles and the rank of the controllability matrix is 4.

The question are: how many state has the sistem?
Is it controllable?
Is it observable?

My solution were...the number of state is at least 4.
If it's of 4th order, then it's controllable, but not observable.
If is of higher order...no idea!
 
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I agree with your answer. There are three observable and four controllable modes.
 

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