Delay-Variation-Dependent Criteria on Extended Dissipativity for Discrete-Time Neural Networks With Time-Varying Delay

This article is concerned with the extended dissipativity of discrete-time neural networks (NNs) with time-varying delay. First, the necessary and sufficient condition on matrix-valued polynomial inequalities reported recently is extended to a general case, where the variable of the polynomial does not need to start from zero. Second, a novel Lyapunov functional with a delay-dependent Lyapunov matrix is constructed by taking into consideration more information on nonlinear activation functions. By employing the Lyapunov functional method, a novel delay and its variation-dependent criterion are obtained to investigate the effects of the time-varying delay and its variation rate on several performances, such as H_\infty performance, passivity, and l_{2}-l_\infty performance, of a delayed discrete-time NN in a unified framework. Finally, a numerical example is given to show that the proposed criterion outperforms some existing ones.