Input-to-state stability of discrete-time memristive neural networks with two delay components

In this paper, a dynamic delay interval method is utilized to deal with the input-to-state stability problem of discrete-time memristive neural networks (DMNNs) with two delay components. This method relaxes the restriction on upper and lower bounds of the DMNNs delay intervals, which extends the fixed interval of a time-varying delay to a dynamic one. First, a tractable model of DMNNs is obtained via using semidiscretization technique. Furthermore, by constructing several novel Lyapunov-Krasovskii functionals, free-weighting matrices and using some techniques such as Refined Jensen-based inequalities, mathematical induction, we obtain some new sufficient conditions in the form of linear matrix inequality to ensure that the considered DMNNs with two time-varying delays are input-to-state stable. The input-to-state stability criteria for the DMNNs with two time-invariant delays are also provided. Finally, two numerical examples are presented to demonstrate the effectiveness of our theoretical results. (C) 2018 Elsevier B.V. All rights reserved.