New results on stability analysis and extended dissipative conditions for uncertain memristive neural networks with two additive time‐varying delay components and reaction‐diffusion terms
Tao Wu, Jinde Cao, Lianglin Xiong, Xueqin Xie
Abstract
Summary This article deals with the problems of exponential stability and extended dissipative analysis for a class of uncertain memristive neural networks (MNNs) with additive time‐varying delays and reaction‐diffusion terms. On the basis of generalized Lyapunov functional approach, Hardy‐Poincarè inequality, Jensen's inequality, as well as some other inequality techniques, it is shown that the issues of exponential stability and extended dissipativity for the uncertain reaction‐diffusion MNNs are solvable if a set of linear matrix inequalities (LMIs) proposed are feasible. As a special case, the conditions on exponential stability and extended dissipativity for the uncertain MNNs with additive time‐varying delays are also obtained and given in terms of nonlinear matrix inequalities (NMIs). The obtained NMIs can be transformed as general LMIs via using a new quadratic convex combination skill. Moreover, the developed sufficient conditions for the uncertain delayed MNNs with and without reaction‐diffusion terms can be easily checked by Matlab LMI control toolbox, and three numerical examples with simulation are provided to show the effectiveness and applicability of the theoretical results.