Stability in impulsive Cohen-Grossberg-type BAM neural networks with distributed delays

In this paper, a class of impulsive Cohen-Grossberg-type bi-directional associative memory (BAM) neural networks with distributed delays is investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing the homeomorphism theory, the M-matrix theory and inequality technique, some new general sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive Cohen-Grossberg-type BAM neural networks with distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the system parameters and impulsive disturbed intension. An example is given to show the effectiveness of the results obtained here.     

Network synchronization under distributed delayed impulsive control: Average delayed impulsive weight approach

This paper mainly investigates synchronization of complex dynamical networks (CDNs) with both system delay and coupled delay through distributed delayed impulsive control. Instead of constraining the impulsive weight and impulsive delay one by one, a new concept of average delayed impulsive weight is proposed to obtain more relaxed conditions. Subsequently, based on the impulsive control topology, Lyapunov theory and linear matrix inequality (LMI) design, certain flexible criteria of global exponential synchronization (GES) are given and the corresponding convergence rate is estimated. It is interesting to see that the CDNs can still achieve synchronization under comprehensive conditions though impulsive weights work negatively. Namely, the delays in impulsive control are able to promote synchronization potentially. Finally, simulations are given to show that the distributed delayed impulsive control can not only speeds up the convergence rate for synchronized networks, but also facilitates synchronization for desynchronized networks. In addition, the obtained results can be applied to unmanned craft systems.     

Global exponential stability of impulsive discrete-time neural networks with time-varying delays

This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria.     

Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays

This paper is concerned with the existence and global exponential stability of periodic solution for a class of impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays. Some sufficient conditions ensuring the existence and global exponential stability of periodic solution are derived by constructing a suitable Lyapunov function and a new differential inequality. The proposed method can also be applied to study the impulsive Cohen-Grossberg-type BAM neural networks with finite distributed delays. The results in this paper extend and improve the earlier publications. Finally, two examples with numerical simulations are given to demonstrate the obtained results.     

Stability analysis of impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms

In this paper, we investigate a class of impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms. By establishing an integro-differential inequality with impulsive initial conditions and applying M-matrix theory, we find some sufficient conditions ensuring the existence, uniqueness, global exponential stability and global robust exponential stability of equilibrium point for impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms. An example is given to illustrate the results obtained here.     

Delay-dependent exponential stability for impulsive Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms

In this paper, a class of impulsive Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion is formulated and investigated. By employing delay differential inequality and the linear matrix inequality (LMI) optimization approach, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive Cohen–Grossberg neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of Cohen–Grossberg neural networks. An example is given to show the effectiveness of the results obtained here.     

Exponential stability of Hopfield neural networks with time‐varying delays via impulsive control

In this paper, by utilizing the Lyapunov functionals, the analysis method and the impulsive control, we analyze the exponential stability of Hopfield neural networks with time‐varying delays. A new criterion on the exponential stabilization by impulses and the exponential stabilization by periodic impulses is gained. We can see that impulses do contribution to the system's exponential stability. Two examples are given to illustrate the effectiveness of our result. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamical analysis of impulsive neural networks with time‐varying delays

In this work, a new criterion concerning the global exponential stability of impulsive neural networks with time‐varying delays is presented by employing the impulsive delayed differential inequality method. The criterion is independent of the time‐varying delays and does not require the differentiability of delay functions. An example and its simulation showing the effectiveness of the present criterion is given finally. Copyright © 2012 John Wiley & Sons, Ltd.     

Synchronization of switched neural networks with mixed delays via impulsive control

This paper concerns the problem of global exponential synchronization for a class of switched neural networks with time-varying delays and unbounded distributed delays via impulsive control method. By using Lyapunov stability theory, new synchronization criterion is derived. In our synchronization criterion, the switching law can be arbitrary and the concept of average impulsive interval is utilized such that the obtained synchronization criterion is less conservative than those based on maximum of impulsive intervals. Numerical simulations are given to show the effectiveness and less conservativeness of the theoretical results.     

Mean square exponential synchronization for impulsive coupled neural networks with time‐varying delays and stochastic disturbances

In this article, the mean square exponential synchronization of a class of impulsive coupled neural networks with time‐varying delays and stochastic disturbances is investigated. The information transmission among the systems can be directed and lagged, that is, the coupling matrices are not needed to be symmetrical and there exist interconnection delays. The dynamical behaviors of the networks can be both continuous and discrete. Specially, the time‐varying delays are taken into consideration to describe the impulsive effects of the system. The control objective is that the trajectories of the salve system by designing suitable control schemes track the trajectories of the master system with impulsive effects. Consequently, sufficient criteria for guaranteeing the mean square exponential convergence of the two systems are obtained in view of Lyapunov stability theory, comparison principle, and mathematical induction. Finally, a numerical simulation is presented to show the verification of the main results in this article. © 2015 Wiley Periodicals, Inc. Complexity 21: 190–202, 2016     

Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms

In this paper, the global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms is considered. By establishing an integro-differential inequality with impulsive initial condition and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, several new sufficient conditions are obtained to ensure the global exponential stability of the equilibrium point for fuzzy cellular neural networks with delays and reaction-diffusion terms. These results extend and improve the earlier publications. Two examples are given to illustrate the efficiency of the obtained results.     

Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays

In this paper, by means of constructing the extended impulsive delayed Halanay inequality and by Lyapunov functional methods, we analyze the global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays. Some new sufficient conditions ensuring exponential stability of the unique equilibrium point of impulsive Hopfield neural networks with time delays are obtained. Those conditions are more feasible than that given in the earlier references to some extent. Some numerical examples are also discussed in this work to illustrate the advantage of the results we obtained.     

具有脉冲和无限时滞的模糊细胞神经网络的全局指数稳定性

In this paper,the global exponential stability of fuzzy cellular neural networks with impulses and infinite delays is investigated.Based on an impulsive delayed integro-differential inequality and the properties of fuzzy logic operation and M-matrix,an easily verified sufficient condition is obtained.Moreover,the exponential convergent rate for the fuzzy cellular neural networks with impulses and infinite delays is also given.An example is given to illustrate the effectiveness of our theoretical result.     

Exponential p-stability of delayed Cohen–Grossberg-type BAM neural networks with impulses

An impulsive Cohen–Grossberg-type bidirectional associative memory (BAM) neural networks with distributed delays is studied. Some new sufficient conditions are established for the existence and global exponential stability of a unique equilibrium without strict conditions imposed on self regulation functions. The approaches are based on Laypunov–Kravsovskii functional and homeomorphism theory. When our results are applied to the BAM neural networks, our results generalize some previously known results. It is believed that these results are significant and useful for the design and applications of Cohen–Grossberg-type bidirectional associative memory networks.     

On the global exponential stability of impulsive functional differential equations with infinite delays or finite delays

This paper considers the impulsive functional differential equations with infinite delays or finite delays. Some new sufficient conditions are obtained to guarantee the global exponential stability by employing the improved Razumikhin technique and Lyapunov functions. The result extends and improves some recent works. Moreover, the obtained Razumikhin condition is very simple and effective to implement in real problems and it is helpful to investigate the stability of delayed neural networks and synchronization problems of chaotic systems under impulsive perturbation. Finally, a numerical example and its simulation is given to show the effectiveness of the obtained result in this paper.     

Stochastic global exponential stability for neutral-type impulsive neural networks with mixed time-delays and Markovian jumping parameters

This paper investigates the problem of the global exponential stability for neutral-type impulsive neural networks with mixed delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays and the jumping parameters are generated from a continuous time discrete state homogenous Markov process. Based on the Lyapunov functional, a sufficient criterion is derived in terms of linear matrix equality (LMI).     

Stability analysis of impulsive delayed switched systems and applications

In this paper, a general class of impulsive delayed switched systems is considered. By employing the Lyapunov–Razumikhin method and some analysis techniques, we established several global asymptotic stability and global exponential stability criteria for the considered impulsive delayed switched systems, which improve and extend some recent works. As an application, the result of global exponential stability are used to study a class of uncertain linear switched systems with time‐varying delays. Several LMI‐based conditions are proposed to guarantee the global robust stability and global exponential stabilization. The designed memoryless state feedback controller can be easily checked by the LMI toolbox in Matlab. Moreover, the dwell time constraint is imposed for the switching law. Finally, two numerical examples and their simulations are given to show the effectiveness of our proposed results. Copyright © 2012 John Wiley & Sons, Ltd.     

Exponential convergence estimates for neural networks with discrete and distributed delays

In this paper, the problems of determining the global exponential stability and estimating the exponential convergence rate are investigated for a class of neural networks with mixed discrete and distributed time-varying delays. By employing a new Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is exploited to establish sufficient easy-to-test conditions for the neural networks to be globally exponentially stable, which can be readily solved by using the numerically efficient Matlab LMI toolbox. Three numerical examples are provided to demonstrate the effectiveness of the proposed results.     

Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays

In this paper, the global exponential stability for neutral-type impulsive neural networks with discrete and distributed delays is established by utilizing the Lyapunov–Krasovskii functional combining with the linear matrix inequality(LMI) approach.