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We investigate singular perturbation problems caused by small delays in theview of pseudo-exponential dichotomy. For a general linear non-autonomousretarded differential equation with small delay, previous works established theexistence of a pseudo-exponential dichotomy. The main objective of this paperis to give a detailed analysis of three splitting properties of this dichotomy.By obtaining serval new estimates and giving the explicit expressions of thebounds and the exponents associated with this dichotomy, we prove that as thedelay tends to zero, the spectral gap approaches to infinity, and the angulardistance and the separation index associated with this dichotomy are boundedfrom below by a positive constant which is independent of the delay.

Splitting properties of linear differential systems with small delays