Stability Conditions of a Class of Linear Retarded Differential Systems

Abstract

In this paper, we give some new necessary and sufficient conditions for the asymptotic stability of a linear retarded differential system with two delays x (t) + (1 − a) x (t) + A (x (t − k) + x (t − l)) = 0, t ≥ 0, where a < 1 is a real number, A is a 2 × 2 real constant matrix, and k, l are positive numbers such that k > l.