New Results on Stability and Passivity for Discrete-Time Neural Networks with a Time-Varying Delay

This paper is concerned with the stability and passivity problem for the discrete-time neural networks with a time-varying delay. A new delay-product-type Lyapunov–Krasovskii functional is constructed by fully considering the information on the state and activation function. By developing a new delay-variation-dependent reciprocally convex combination lemma, a novel stability condition is derived that is shown to be more relaxed than some of existing stability conditions through numerical examples. For the case that the bounds of the delay variation are unavailable, the corresponding stability condition is also derived. Furthermore, the passivity problem is investigated for the delayed discrete-time neural networks. The results can be applied to stability analysis and control of power grids and time-delay robotic systems.