title: Asymptotic stability for neural networks with mixed time-delays: the discrete-time case.
abstract: This paper is concerned with the stability analysis problem for a new class of discrete-time recurrent neural networks with mixed time-delays. The mixed time-delays that consist of both the discrete and distributed time-delays are addressed, for the first time, when analyzing the asymptotic stability for discrete-time neural networks. The activation functions are not required to be differentiable or strictly monotonic. The existence of the equilibrium point is first proved under mild conditions. By constructing a new Lyapnuov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the discrete-time neural networks to be globally asymptotically stable. As an extension, we further consider the stability analysis problem for the same class of neural networks but with state-dependent stochastic disturbances. All the conditions obtained are expressed in terms of LMIs whose feasibility can be easily checked by using the numerically efficient Matlab LMI Toolbox. A simulation example is presented to show the usefulness of the derived LMI-based stability condition.
authors.affiliation: Department of Mathematics, Yangzhou University, Yangzhou 225002, PR China. liuyurong@gmail.com
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: D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D016014:Linear Models; D016571:Neural Networks, Computer; D013269:Stochastic Processes; D013997:Time Factors