SpringerOpen, Advances in Difference Equations, 1(2016), 2016
DOI: 10.1186/s13662-016-0829-z
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Abstract This paper proposes an improved stability condition of discrete-time systems with variable delays. Based on some mathematical techniques, a series of new summation inequalities are obtained. These new inequalities are less conservative than the Jensen inequality. Based on these new summation inequalities and the reciprocally convex combination inequality, a novel sufficient criterion on asymptotical stability of discrete-time systems with variable delays is obtained by constructing a new Lyapunov-Krasovskii functional. The advantage of the proposed inequality in this paper is demonstrated by a classical example from the literature.