Abstract
We consider the problem of constructing observers for linear systems with commensurate time delays. We construct two types of observers.
One is derived from the duality to the stabilization problem of the systems with commensurate time delays.
Another is derived from the following method. That is, if we can transform some system over polynomial ring to make a stable error system, we can construct a new type of observers. The condition for constructibility of this type of observer is attributed to the condition for solvability of some matrix algebraic equation over polynomial ring.
Every observer discussed in this paper coincides in its constructibility condition.
