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The paper explores asymptotic stability of discrete-time linear systems whose system matrix belongs to the convex combination of given vertex matrices, and time-varying parameters of this combination lie in a polyhedral domain. The paper presents a criterion written in LMIs to test the asymptotic stability based on time-varying parameter-dependent Lyapunov function. Comparing with the quadratic stability and the constant parameter-dependent Lyapunov function approaches, our result not only reduces the conservation to a lower level, but also leads to previous results as our corollaries. At last, an example calculated as compared with known approaches shows the advantage of ours.