In this paper, the exponential stability problem of a class of linear non-autonomous systems with continuously distributed multiple time-varying delays is studied. Based on the Lyapunov-Krasovskii functional approach, sufficient conditions for the exponential stability of the system are established via the solution of Riccati differential inequalities. By using this generalized result, new sufficient conditions are derived for the robust stability and stabilization of the systems subjected to uncertainties and external controls. Illustrative numerical examples are given to indicate significant improvements of the results.