Number of poles and rank of controllability matrix

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SUMMARY

The discussion centers on a control system with a transfer function exhibiting three poles and a controllability matrix rank of four. It is established that the system must have at least four states. The system is deemed controllable due to the rank of the controllability matrix exceeding the number of poles, but it is not observable if it is of fourth order. For higher-order systems, the observability status remains uncertain.

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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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