title: Global exponential stability of generalized recurrent neural networks with discrete and distributed delays.
abstract: This paper is concerned with analysis problem for the global exponential stability of a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, by employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the RNNs to be globally exponentially stable. Therefore, the global exponential stability of the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.
authors.affiliation: Department of Mathematics, Yangzhou University, Yangzhou 225002, People's Republic of China.
authors.forename: Yurong
authors.initials: Y
authors.lastname: Liu
authors.forename: Zidong
authors.initials: Z
authors.lastname: Wang
authors.forename: Xiaohui
authors.initials: X
authors.lastname: Liu
mesh_terms: D001185:Artificial Intelligence; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D010363:Pattern Recognition, Automated / Q000379:methods; D013997:Time Factors