Stability and robust stability of non-autonomous linear differential equations with infinite delay

Abstract

By the idea of comparison principle, we first introduce novel explicit criteria for the $ \varrho $-stability of general linear non-autonomous functional differential equations with infinite delay. Some characterizations for the time-independent exponential stability are also investigated. We then present a sufficient condition for the exponential stability of the equations subject to time-varying structured perturbations. These results lead to applications to the linear non-autonomous differential system with unbounded delay and the linear non-autonomous integro-differential equations with delay. Some examples are given to illustrate the obtained results.