  In this paper, stability analysis of time delay systems is considered based
on decomposition of the systems to subsystems. The decomposition process needs
matrices of these systems to be simultaneously block triangularize. We show
that a finite set of matrices are simultaneously block triangularize if and
only if they have a common invariant subspace. The importance of the
decomposition is highlighted by some systems that their characteristic equation
has repeated roots on the imaginary axis. For such systems, the cluster
treatment method and the direct method cannot be employed to analyze the
stability of them, unless, we decompose the systems to subsystems. On the other
hand, it has been shown that stabilization of time delay systems can be done by
delayed feedback. Moreover, this kind of feedback is applied to design a
controller.
