Criteria for stability in approximate delay systems

This paper introduces some results about stability for a class of linear point-delayed systems and how to compute these results. This work uses some theorems on stability for delayed systems due to Mori [1–3]. Our method consists basically in finding extensions of such results to the case of an approximate representation of the linear delayed system, i.e., under which circumstances stability for an approximate representation of the delayed system implies stability for the exact (real) delayed system. Sufficient conditions for asymptotic stability of linear delayed systems are greatly simplified and straightforwardly computed under Taylor series representation of the system state equations. Conditions under which asymptotic stability for the approximate system implies asymptotic stability for the real system are also outlined in the paper.