Improved passivity criteria for memristive neural networks with interval multiple time-varying delays

In this paper, the problem of passivity analysis for memristive neural networks with interval multiple time-varying delays is studied. More precisely, the multiple time-varying delays include not only the time-varying delay in the discrete term but also the time-varying delay in the leakage term. Moreover, this paper provides an improved passivity criteria for neural networks with the above two delays varying in their respective intervals under the joint action of differential inclusions, set-valued maps and Lyapunov theory. By constructing a novel Lyapunov-Krasovskii functional together with triple integral terms and employing first-order reciprocally convex method, second-order reciprocally convex method, free-weighting matrices technique and zero equalities, the improved passivity criteria are derived to guarantee that the input and output of the considered memristive neural networks satisfy a prescribed passivity-inequality constraint. Also it is assumed that the lower bounds of the activation functions can be positive, negative or zero. Meanwhile, it is worth pointing out that all of these criteria can be reduced to be applied not only to the memristive neural networks with only interval time-varying delay in the discrete term but also to the memristive neural networks with both multiple time-varying delays not containing interval terms. Further, the obtained conditions are formulated in terms of linear matrix inequalities which can be easily solved by using some standard numerical packages. Finally, two numerical examples are given to show the effectiveness and less conservatism of the proposed criteria. (C) 2015 Elsevier B.V. All rights reserved.