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

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 LyapunovKrasovskii 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.