Electronic Journal of Differential Equations, Vol. 2005(2005), No. 58, pp. 1-8. Title: Exponential stability criteria of linear non-autonomous systems with multiple delays Authors: Vu Ngoc Phat (Institute of Math., Hanoi, Vietnam) Phan T. Nam (Institute of Math., Hanoi, Vietnam) Abstract: In this paper, we study the exponential stability of linear non-autonomous systems with multiple delays. Using Lyapunov-like function, we find sufficient conditions for the exponential stability in terms of the solution of a Riccati differential equation. Our results are illustrated with numerical examples. Submitted November 12, 2004. Published June 6, 2005. Math Subject Classifications: 34K20. Key Words: Exponential stability; time-delay; Lyapunov function; Riccati equation