The stability robustness of linear-variant systems in the time domain is considered using the Lyapunov approach and the maximum singular values of a time-variant matrix. Bounds on linear time-varying perturbations that maintain the stability of a uniformly asymptotically stable linear time-variant system are obtained for both unstructured and structured independent perturbations. Bounds are also derived assuming that various elements of the system matrix are perturbed dependency. The result for the structural perturbation case is extended to the stability analysis of time-variant interval matrices.