In this paper we analyse the stability robustness of linear discrete-time systems which are described by a state-space model but are perturbed with structured time-varying uncertainty. We present new Lyapunov stability robustness bounds in which the freedom of the matrixQis utilized more effectively than that used by Kolla et al. (1989) to obtain a larger bound of tolerable time-varying uncertainty, and the similarity transformation is employed more directly and usefully than that proposed by Kolla and Farison (1990) to reduce conservation. Further, the relationship between the matrixQand the similarity transformation matrix M is given. Improvements are illustrated by an application of our proposed method to a macroeconomic system