This paper addresses theoretical limitations in Lyapunov-Krasovskii methods for time-varying delay systems through three principal contributions. First, a novel delay-dependent inequality for the derivatives of the Lyapunov function is proposed, which fundamentally distinguishes our approach from classical Halanay-type inequalities through explicit time-varying parameterization. An enhanced prescribed-time stability theorem for Filippov systems with time-varying delays and uncertainties is estab