Abstract: The problem of robust stability analysis for convex polytopic uncertain discrete-time systems with multiple-state delays is investigated.Based on the parameter-dependent Lyapunov stability and linear matrix inequality,the sufficient condition for robust stability is derived to enable the systems with delays to be robustly stable.With this condition,robust stability verification for the systems can be accomplished by testing the feasibility of a set of linear matrix inequalities.Due to the idea of parameter-dependent Lyapunov stability,the obtained robust stability condition has less conservativeness than the one based on quadratic stability.Numerical examples validate the results.