Hierarchical Stability Conditions for a Class of Generalized Neural Networks With Multiple Discrete and Distributed Delays.

Abstract

This brief investigates the analysis issue for global asymptotic stability of a class of generalized neural networks with multiple discrete and distributed delays. To tackle delays arising in different neuron activation functions, we employ a generalized model with multiple discrete and distributed delays which covers various existing neural networks. We then generalize the Bessel-Legendre inequalities to deal with integral terms with any linearly independent functions and nonlinear function of states. Based on these inequalities, we design the Lyapunov-Krasovskii functional and derive hierarchical linear matrix inequality stability conditions. Finally, three numerical examples are provided to demonstrate that the proposed method is less conservative with a reasonable numerical burden than the existing results.