The robust stability problem for uncertain, linear, state-space models is considered. When a fixed Lyapunov function is used to provide an admissible perturbation set, the obtained variation bounds can be too conservative. The main purpose of this investigation is to define the conditions, under which it is always possible to construct a parameter-dependent Lyapunov function for a class of uncertain systems. The contribution to robustness study is due to a new sufficient condition for robust stability. The advantages of this approach are illustrated by examples and comparison with results, obtained by known procedures is made.