In practical applications, stochastic effects are normally viewed as the major sources that lead to the system’s unwilling behaviours when modelling real neural systems. As such, the research on network models with stochastic effects is significant. In view of this, in this paper, we analyse the issue of robust stability for a class of uncertain complex-valued stochastic neural networks (UCVSNNs) with time-varying delays. Based on the real-imaginary separate-type activation function, the original UCVSNN model is analysed using an equivalent representation consisting of two real-valued neural networks. By constructing the proper Lyapunov–Krasovskii functional and applying Jensen’s inequality, a number of sufficient conditions can be derived by utilizing It $\widehat{o}$ ’s formula, the homeomorphism principle, the linear matrix inequality, and other analytic techniques. As a result, new sufficient conditions to ensure robust, globally asymptotic stability in the mean square for the considered UCVSNN models are derived. Numerical simulations are presented to illustrate the merit of the obtained results.

In this manuscript, we consider the finite-time $H_{\infty }$ control for nonlinear systems with time-varying delay. With the assistance of a novel Lyapunov-Krasovskii functional which includes some integral terms, a matrix-based on quadratic convex approach, combined with Wirtinger inequalities and some useful integral inequalities, a sufficient condition of finite-time boundedness is established. A novel feature presents in this paper is that the restriction which is necessary for the upper bound derivative is not restricted to less than 1. Further a $H_{\infty }$ controller is designed via memoryless state feedback control and a new sufficient conditions for the existence of finite-time $H_{\infty }$ state feedback for the system are given in terms of linear matrix inequalities (LMIs). At the end, some numerical examples with simulations are given to illustrate the effectiveness of the obtained result.

In this paper, we consider H ∞ control problem for a class Hopfield neural networks with interval time-varying delay. The time delay is a continuous function belonging to a given interval, but not necessariry differentiable. The stabilizing controllers to be designed must satisfy some exponential stability constraints on the closed-loop poles. Based on the construction of improved Lyapunov-Krasovskii functionals combined with Newton-Leibniz formula. H ∞ controller is designed via memoryless state feedback control and new sufficient conditions for the existence of the H ∞ state-feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.