This paper deals with the robust stability analysis and robust control synthesis with H-infinity guaranteed performance index for time-invariant uncertain neutral systems based on linear matrix inequalities (LMIs). The novelty is to extend the discretisation technique introduced by K. Gu for an appropriate parameter-dependent Lyapunov-Krasovskii functional. Then, the approach proposed improves the previous criteria from the literature that treats robust stability and H-infinity control for uncertain neutral systems. The main strategy used to derive the obtained conditions is to introduce slack variables allowing one to decouple the system matrices from the Lyapunov functional matrices, without including additional dynamics. Two numerical examples are performed to support the theoretical predictions. The first example deals with stability analysis and the other illustrates how the proposed approach may provide a better solution for the H-infinity guaranteed cost control problem when compared with others available in the literature.