Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling

This paper investigates the problem of master-slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals. An improved method is proposed, which captures the characteristic of sampled-data systems. Some delay-dependent criteria are derived to ensure the exponential stability of the error systems, and thus the master systems synchronize with the slave systems. The desired sampled-data controller can be achieved by solving a set of linear matrix inequalitys, which depend upon the maximum sampling interval and the decay rate. The obtained conditions not only have less conservatism but also have less decision variables than existing results. Simulation results are given to show the effectiveness and benefits of the proposed methods.

Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects

This paper focuses on the hybrid effects of parameter uncertainty, stochastic perturbation, and impulses on global stability of delayed neural networks. By using the Ito formula, Lyapunov function, and Halanay inequality, we established several mean-square stability criteria from which we can estimate the feasible bounds of impulses, provided that parameter uncertainty and stochastic perturbations are well-constrained. Moreover, the present method can also be applied to general differential systems with stochastic perturbation and impulses.

Estimating the ultimate bound and positively invariant set for a class of Hopfield networks

In this paper, we investigate the ultimate bound and positively invariant set for a class of Hopfield neural networks (HNNs) based on the Lyapunov stability criterion and Lagrange multiplier method. It is shown that a hyperelliptic estimate of the ultimate bound and positively invariant set for the HNNs can be calculated by solving a linear matrix inequality (LMI). Furthermore, the global stability of the unique equilibrium and the instability region of the HNNs are analyzed, respectively. Finally, the most accurate estimate of the ultimate bound and positively invariant set can be derived by solving the corresponding optimization problems involving the LMI constraints. Some numerical examples are given to illustrate the effectiveness of the proposed results.