Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays

In this Letter, the passivity problem of uncertain neural networks with discrete and distributed time-varying delays is investigated. New delay-dependent conditions for this problem are obtained by using a novel Lyapunov functional together with the linear matrix inequality (LMI) approach. Numerical examples are given to show the effectiveness of our theoretical results.     

Synchronization criteria for coupled Hopfield neural networks with time-varying delays

This paper proposes new delay-dependent synchronization criteria for coupled Hopfield neural networks with time-varying delays. By construction of a suitable Lyapunov-Krasovskii's functional and use of Finsler's lemma, novel synchronization criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Stability analysis of neural networks with interval time-varying delays

The global exponential stability is investigated for neural networks with interval time-varying delays. Based on the Leibniz-Newton formula and linear matrix inequality technique, delay-dependent stability criteria are proposed to guarantee the exponential stability of neural networks with interval time-varying delays. Some numerical examples and comparisons are provided to show that the proposed results significantly improve the allowable upper and lower bounds of delays over some existing ones in the literature.     

Synchronization of stochastically hybrid coupled neural networks with coupling discrete and distributed time-varying delays

A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.     

Exponential stability of cellular neural networks with multiple time delays and impulsive effects

In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality （LMI） and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.     

Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays

In this paper, the problem of stability analysis for a class of impulsive stochastic Cohen-Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen-Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.     

Stability conditions for Cohen-Grossberg neural networks with time-varying delays

Global asymptotic stability for Cohen-Grossberg neural networks (CGNNs) with time-varying delays is investigated. Criteria are proposed to guarantee the stability and uniqueness of equilibrium point of CGNNs via LMI approach. A numerical example is illustrated to show the effectiveness of our results.     

Polynomial synchronization of complex-valued inertial neural networks with multi-proportional delays

This paper investigates the polynomial synchronization (PS) problem of complex-valued inertial neural networks with multi-proportional delays. It is analyzed based on the non-separation method. Firstly, an exponential transformation is applied and an appropriate controller is designed. Then, a new sufficient criterion for PS of the considered system is derived by the Lyapunov function approach and some inequalities techniques. In the end, a numerical example is given to illustrate the effectiveness of the obtained result.     

Global point dissipativity of neural networks with mixed time-varying delays

By employing the Lyapunov method and some inequality techniques, the global point dissipativity is studied for neural networks with both discrete time-varying delays and distributed time-varying delays. Simple sufficient conditions are given for checking the global point dissipativity of neural networks with mixed time-varying delays. The proposed linear matrix inequality approach is computationally efficient as it can be solved numerically using standard commercial software. Illustrated examples are given to show the usefulness of the results in comparison with some existing results.     

Improved delay-dependent stability criterion for neural networks with time-varying delays

In this Letter, the problem of stability analysis for neural networks with time-varying delays is considered. By constructing a new Lyapunov functional, a new delay-dependent stability criterion for the network is established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the effectiveness of proposed criterion.     

Delay-range-dependent stability for fuzzy BAM neural networks with time-varying delays

This Letter considers the problem of delay-range-dependent stability for fuzzy bi-directional associative memory (BAM) neural networks with time-varying interval delays. Based on Lyapunov-Krasovskii theory, the delay-range-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs). By constructing new Lyapunov-Krasovskii functional, stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using some advanced techniques for achieving delay dependence. A numerical example is given to illustrate the effectiveness of the proposed method.     

Global asymptotic stability of fuzzy cellular neural networks with time-varying delays

In this Letter fuzzy cellular neural networks with time-varying delays are studied. Sufficient conditions for the existence, uniqueness and global asymptotic stability of equilibrium point are established by using the theory of topological degree and applying the properties of nonsingular M-matrix. The activation functions are not required to be differentiable, bounded or monotone nondecreasing. The results of this Letter are new and they complement previously known results.     

Robust impulsive synchronization of coupled delayed neural networks with uncertainties

This paper investigates the synchronization scheme of coupled neural networks with time delays. The coupling function, which can be linear or nonlinear, is subject to uncertainties in the network. By utilizing the stability theory for impulsive functional differential equations, several new criteria are obtained to ensure the robust synchronization of coupled networks via impulsive control. Furthermore, an estimation of the predicted stable region is derived to facilitate the design of the control gain. Finally, numerical simulations are presented to demonstrate the effectiveness of our results.     

Attracting and invariant sets of fuzzy Cohen-Grossberg neural networks with time-varying delays

In this Letter, a class of fuzzy Cohen-Grossberg neural networks (FCGNNs) with time-varying delays is investigated. With removing some restrictions on the amplification functions, a new nonlinear delay differential inequality is established, which improves previously known criteria. By using the properties of M-cone and a generalization of Barbǎlat's lemma, the boundedness and asymptotic behavior for the solution of the inequality are obtained. Applying this nonlinear delay differential inequality, a series of new and useful criteria are obtained to ensure the existence of global attracting set and invariant set for FCGNNs with time-varying delays. An example is given to illustrate the effectiveness of our results.     

New results on stability criteria for neural networks with time-varying delays

In this paper,the problem of stability analysis for neural networks with time-varying delays is considered.By constructing a new augmented Lyapunov-Krasovskii’s functional and some novel analysis techniques,improved delaydependent criteria for checking the stability of the neural networks are established.The proposed criteria are presented in terms of linear matrix inequalities(LMIs) which can be easily solved and checked by various convex optimization algorithms.Two numerical examples are included to show the superiority of our results.     

Delay-dependent exponential stability for neural networks with discrete and distributed time-varying delays

This Letter studies the exponential stability for a class of neural networks (NNs) with both discrete and distributed time-varying delays. Under weaker assumptions on the activation functions, by defining a more general type of Lyapunov functionals and developing a new convex combination technique, new less conservative and less complex stability criteria are established to guarantee the global exponential stability of the discussed NNs. The obtained conditions are dependent on both discrete and distributed delays, are expressed in terms of linear matrix inequalities (LMIs), and contain fewer decision variables. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed conditions.     

Robust stability analysis of Takagi-Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays

In this paper,the global stability of Takagi-Sugeno (TS) uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays (TSUSFRNNs) is considered.A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs.The proposed stability conditions are demonstrated through numerical examples.Furthermore,the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed.Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature.     

Dynamic behaviors of almost periodic solution of discrete-time inertial neural networks with delays

A type of discrete-time inertial neural networks with delays is considered. Using the contraction mapping principal, we obtain the existence of almost periodic sequence solution for the considered system. Furthermore, several sufficient conditions are obtained for the boundness and global attractivity of almost periodic sequence solution by using difference equation analysis techniques.     

Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays

In this Letter, by utilizing the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of uncertain stochastic fuzzy Bidirectional Associative Memory (BAM) neural networks with time-varying delays which are represented by the Takagi-Sugeno (TS) fuzzy models. A new class of uncertain stochastic fuzzy BAM neural networks with time varying delays has been studied and sufficient conditions have been derived to obtain conservative result in stochastic settings. The developed results are more general than those reported in the earlier literatures. In addition, the numerical examples are provided to illustrate the applicability of the result using LMI toolbox in MATLAB.