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 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.

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The global exponential stability for bidirectional associative memory neural networks with time-varying delays is studied. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative, or zero. By constructing new and improved Lyapunov-Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential stability for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI). Numerical examples are given to demonstrate that the derived condition is less conservative than some existing results given in the literature.

In this paper, the global exponential stability for the neutral-type inertial bidirectional association memory neural networks with time-varying delays is considered. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative or zero. By constructing new and improved Lyapunov-Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent the neutral-type inertial bidirectional association memory neural networks with time-varying delays is derived in the form of linear matrix.

<abstract><p>The summation inequality is essential in creating delay-dependent criteria for discrete-time systems with time-varying delays and developing other delay-dependent standards. This paper uses our rebuilt summation inequality to investigate the robust stability analysis issue for discrete-time neural networks that incorporate interval time-varying leakage and discrete and distributed delays. It is a novelty of this study to consider a new inequality, which makes it less conservative than the well-known Jensen inequality, and use it in the context of discrete-time delay systems. Further stability and passivity criteria are obtained in terms of linear matrix inequalities (LMIs) using the Lyapunov-Krasovskii stability theory, coefficient matrix decomposition technique, mobilization of zero equation, mixed model transformation, and reciprocally convex combination. With the assistance of the LMI Control toolbox in Matlab, numerical examples are provided to demonstrate the validity and efficiency of the theoretical findings of this research.</p></abstract>