Relaxed passivity conditions for neural networks with time-varying delays

This paper revisits the problem of passivity analysis for neural networks with time-varying delays. A new delay-dependent criterion is obtained in terms of linear matrix inequalities, guaranteeing that the input and output of the considered neural network satisfy a prescribed passivity-inequality constraint. This newly presented criterion does not require all the symmetric matrices involved in the employed quadratic Lyapunov–Krasovskii functional to be positive definite. This feature is remarkable since it sheds new light on the traditional ideas for constructing Lyapunov–Krasovskii functionals. More importantly, the conservatism of delay-dependent passivity conditions can be reduced due to the relaxation on the positive-definiteness of every Lyapunov matrix. It is shown both theoretically and numerically that the passivity criterion proposed in this paper is truly less conservative than some of the latest results in the literature.