Criteria for stability of linear dynamical systems with multiple delays by fixed point

Abstract

In this study we considered a linear Dynamical system with multiple delays and find suitable conditions on the systems parameters such that for a given initial function, we can define a mapping in a carefully chosen complete metric space on which the mapping has a unique fixed point. An asymptotic stability theory for the zero solution with necessary and sufficient condition is proved by means of the contraction mapping principle.

Keywords: Fixed points, Stability, Multiple delays