It is well known that the maximum amplitude of the estimation error of a full order observer becomes extremely large as all the poles approach infinity in the left half complex plane (LHP).
In this paper we clarify the asymptotic behavior of a full order observer for the case where a part of the poles approach infinity in LHP.
First, we show that the dimension m of the outputs is equivalent to the number of poles which can approach infinity in LHP without diverging of the initial estimation error. Next, we prove that the full order observer converges to a minimal order observer except the initial state as the m poles tend to infinity in LHP. Finally, we investigate a full order observer estimating a linear function of the state variable under the condition that a part of the poles approach infinity in LHP. The obtained result is considered as an extention of Mita's result under the condition on all the poles.