Global asymptotic stability of complex-valued neural networks with additive time-varying delays

Stability and synchronization for complex-valued neural networks with stochastic parameters and mixed time delays

In this paper, a class of complex-valued neural networks (CVNNs) with stochastic parameters and mixed time delays are proposed. The random fluctuation of system parameters is considered in order to describe the implementation of CVNNs more practically. Mixed time delays including distributed delays and time-varying delays are also taken into account in order to reflect the influence of network loads and communication constraints. Firstly, the stability problem is investigated for the CVNNs. In virtue of Lyapunov stability theory, a sufficient condition is deduced to ensure that CVNNs are asymptotically stable in the mean square. Then, for an array of coupled identical CVNNs with stochastic parameters and mixed time delays, synchronization issue is investigated. A set of matrix inequalities are obtained by using Lyapunov stability theory and Kronecker product and if these matrix inequalities are feasible, the addressed CVNNs are synchronized. Finally, the effectiveness of the obtained theoretical results is demonstrated by two numerical examples.

Non-fragile output-feedback synchronization for delayed discrete-time complex-valued neural networks with randomly occurring uncertainties

This paper is step forward to establish an exponential synchronization criterion for discrete-time complex-valued neural networks (CVNNs) having time-varying delays subject to randomly occurring uncertain weighting parameters, in order to overcome the fluctuation when the output-feedback controller imposes on its dynamics. To achieve this, Jensen's weighted summation inequalities (WSIs) and an extended reciprocal convex matrix inequality (ERCMI) are extended into the domain of complex field. By introducing some augmented vectors, a Lyapunov-Krasovskii functional (LKF) is constructed to attain an improved delay-dependent linear matrix inequalities (LMIs) constraint for the exponential synchronization phenomenon of the desired master-slave neuronal system model. For instance, the upper bound of the quadratic summation terms occurred in the finite difference of the LKF have been obtained from its linearization that has been made by the developed complex-valued WSIs and complex-valued ERCMI. The proposed results are less restrictive with the minimum number of decision variables than those obtained using existing inequalities. The designed output-feedback control gain has been determined by solving a set of complex-valued LMIs and it has been enforced with a prescribed exponential decay rate. Finally, in sight of MATLAB software, the established results have been examined via a numerical example supported by the simulation results.

Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties

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.

Robust Dissipativity Analysis of Hopfield-Type Complex-Valued Neural Networks with Time-Varying Delays and Linear Fractional Uncertainties

We study the robust dissipativity issue with respect to the Hopfield-type of complex-valued neural network (HTCVNN) models incorporated with time-varying delays and linear fractional uncertainties. To avoid the computational issues in the complex domain, we divide the original complex-valued system into two real-valued systems. We devise an appropriate Lyapunov-Krasovskii functional (LKF) equipped with general integral terms to facilitate the analysis. By exploiting the multiple integral inequality method, the sufficient conditions for the dissipativity of HTCVNN models are obtained via the linear matrix inequalities (LMIs). The MATLAB software package is used to solve the LMIs effectively. We devise a number of numerical models and their empirical results positively ascertain the obtained results.