This work is devoted to the robust stability analysis of linear systems with distributed delays. The approach is based on recent results in the Lyapunov-Krasovskii framework, where a Lyapunov-Krasovskii functional with prescribed negative definite derivative is applied. The stability conditions obtained in this work, are simple inequalities which depend on the so-called delay Lyapunov matrix. The cases of matrix parameters and delays uncertainties are addressed, accurately detecting exact stability bounds when applied in an iterative manner. Our method is used successfully to tackle the challenging problem of robust predictor-based stabilization of systems with state and input delays.