title: Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks.
abstract: This paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete-time neural networks with time-varying delay. The individual neural network is subject to parameter uncertainty, stochastic disturbance, and time-varying delay, where the norm-bounded parameter uncertainties exist in both the state and weight matrices, the stochastic disturbance is in the form of a scalar Wiener process, and the time delay enters into the activation function. For the array of coupled neural networks, the constant coupling and delayed coupling are simultaneously considered. We aim to establish easy-to-verify conditions under which the addressed neural networks are synchronized. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally, robustly, exponentially synchronized in the mean square. The LMI-based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time-varying delay, and can be solved efficiently via the Matlab LMI Toolbox. Two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme.
authors.affiliation: Department of Mathematics, Southeast University, Nanjing 210096, China. jinlliang@gmail.com
authors.forename: Jinling
authors.initials: J
authors.lastname: Liang
authors.forename: Zidong
authors.initials: Z
authors.lastname: Wang
authors.forename: Yurong
authors.initials: Y
authors.lastname: Liu
authors.forename: Xiaohui
authors.initials: X
authors.lastname: Liu
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D015233:Models, Statistical; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D010363:Pattern Recognition, Automated / Q000379:methods*; D012815:Signal Processing, Computer-Assisted; D013269:Stochastic Processes