Abstract
In this paper we consider a method of constructing observers for linear time-invariant, discrete-time systems. The derived results are as follows.
It is assumed that a system S to be observed is completely observable. Then it is shown that an observer for S always can be constructed. And its constructing method is described precisely. The order of the observer is n-m, where n is the order of the state of S and m is that of the output. The number of steps necessary to make the output of the observer coincide with the state of S from the beginning of observation is ν0-1 where ν0 is the observability index of S. This observer is a minimum-time and low-order observing system.
The behavior of this observer is also considered when it is used to observe the linear functions of the state of S.
