Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays

This paper considers the chaotic synchronization problem of neural networks with time-varying and distributed delays using impulsive control method. By utilizing the stability theory for impulsive functional differential equations, several impulsive control laws are derived to guarantee the exponential synchronization of neural networks with time-varying and distributed delays. It is shown that chaotic synchronization of the networks is heavily dependent on the designed impulsive controllers. Moreover, these conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. Finally, a numerical example and its simulation are given to show the effectiveness and advantage of the proposed control schemes.     

Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling

In this paper, the global exponential synchronization is investigated for an array of asymmetric neural networks with time-varying delays and nonlinear coupling, assuming neither the differentiability for time-varying delays nor the symmetry for the inner coupling matrices. By employing a new Lyapunov-Krasovskii functional, applying the theory of Kronecker product of matrices and the technique of linear matrix inequality (LMI), a delay-dependent sufficient condition in LMIs form for checking global exponential synchronization is obtained. The proposed result generalizes and improves the earlier publications. An example with chaotic nodes is given to show the effectiveness of the obtained result.     

Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method

In this paper, an impulsive controller is designed to achieve the exponential synchronization of chaotic delayed neural networks with stochastic perturbation. By using the impulsive delay differential inequality technique that was established in recent publications, several sufficient conditions ensuring the exponential synchronization of chaotic delayed networks are derived, which can be easily checked by LMI Control Toolbox in Matlab. A numerical example and its simulation is given to demonstrate the effectiveness and advantage of the theory results.     

Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction-diffusion

Separate studies have been published on the stability of fuzzy cellular neural networks with time delay in the leakage term and synchronization issue of coupled chaotic neural networks with stochastic perturbation and reaction-diffusion effects. However, there have not been studies that integrate the two fields. Motivated by the achievements from both fields, this paper considers the exponential synchronization problem of coupled chaotic fuzzy cellular neural networks with stochastic noise perturbation, time delay in the leakage term and reaction-diffusion effects using linear feedback control. Lyapunov stability theory combining with stochastic analysis approaches are employed to derive sufficient criteria ensuring the coupled chaotic fuzzy neural networks to be exponentially synchronized. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.     

Exponential stability analysis for uncertain neural networks with interval time-varying delays

In this paper, the problem of exponential stability analysis for neural networks is investigated. It is assumed that the considered neural networks have norm-bounded parametric uncertainties and interval time-varying delays. By constructing a new Lyapunov functional, new delay-dependent exponential stability criteria with an exponential convergence rate are 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 criteria.     

Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: An LMI approach

In this paper, impulsive control for master–slave synchronization schemes consisting of identical chaotic neural networks is studied. Impulsive control laws are derived based on linear static output feedback. A sufficient condition for global asymptotic synchronization of master–slave chaotic neural networks via output feedback impulsive control is established, in which synchronization is proven in terms of the synchronization errors between the full state vectors. An LMI-based approach for designing linear static output feedback impulsive control laws to globally asymptotically synchronize chaotic neural networks is discussed. With the help of LMI solvers, linear output feedback impulsive controllers can be easily obtained along with the bounds of the impulsive intervals for global asymptotic synchronization. The method is finally illustrated by numerical simulations.     

Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay

This paper considers the synchronization problem for coupled neural networks with interval time-varying delays and leakage delay. By construction of a suitable Lyapunov-Krasovskii’s functional and utilization of Finsler’s lemma, novel delay-dependent criteria for the synchronization of 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.     

基于LMI方法的多时滞随机神经网络的指数稳定性

研究了一类具有多个时滞的随机神经网络的均方指数稳定性问题,应用Lyapunov-Krasovskii泛函稳定理论和线性矩阵不等式(LMI)方法,建立了该系统解的指数稳定判别准则,最后通过数值举例阐述了结果的有效性.     

Synchronization of chaotic neural networks with mixed time delays

In this paper, we investigate the synchronization problems of chaotic neural networks with mixed time delays. We first establish the sufficient conditions for synchronization of identical chaotic neural networks with mixed time delays via linear output feedback control. To overcome the difficulty that complete synchronization between nonidentical chaotic neural networks cannot be achieved only by utilizing output feedback control, we use a sliding mode control approach to study the synchronization of nonidentical chaotic neural networks with mixed time delays, where the parameters and functions are mismatched. Numerical simulations are carried out to illustrate the main results.     

A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays

In this paper, the problem of exponential passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing new augmented Lyapunov-Krasovskii’s functionals and some novel analysis techniques, improved delay-dependent criteria for checking the exponential passivity of the neural networks are established. The proposed criteria are represented in terms of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. A numerical example is included to show the superiority of our results.     

Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control

In this paper, a new method to synchronize two identical chaotic recurrent neural networks is proposed. Using the drive-response concept, a nonlinear feedback control law is derived to achieve the state synchronization of the two identical chaotic neural networks. Furthermore, based on the Lyapunov method, a delay independent sufficient synchronization condition in terms of linear matrix inequality (LMI) is obtained. A numerical example with graphical illustrations is given to illuminate the presented synchronization scheme.     

Stochastic exponential synchronization for delayed neural networks with semi-Markovian switchings: Saturated heterogeneous sampling communication

By implementing heterogeneous sampling communication mechanism, this article addresses the exponential synchronization issue of drive–response chaotic neural networks (CNNs) with interval time-varying delays by simultaneously taking into account the semi-Markovian switchings and saturating actuators. More specifically, a semi-Markovian jumping model whose transition rates (TRs) are not constant but depends on the sojourn time (ST) is introduced to characterize the stochastic changing among the interaction of CNNs, which makes the NNs model under consideration more suitable for some actual circumstances. More particularly, we assume that the sampling intervals are heterogeneous and time-varying, which may be more practical in real-life applications than homogeneous sampling policy. Additionally, by introducing some new terms, one novel time-dependent Lyapunov–Krasovskii function (LKF) is ingeniously constructed, which can fully capture the characteristic information of heterogeneous sampling pattern. Benefitting from the introduced relaxed free-weighting matrices (FWM) and resorting to the formed LKF, some sampling-interval-dependent sufficient conditions for controller design of the resulting semi-MJNNs error system are established and expressed by linear matrix inequalities (LMIs). These LMIs-based constraints can be effectively checked by utilizing the available software packages. Therein, the developed synchronization criteria dependent on both the lower and upper bounds of sampling periods, and the available information about the actual sampling pattern is fully considered. Ultimately, two numerical examples are provided to demonstrate the feasibility and practicability of our theoretical findings.     

Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control

-In this paper, we investigate the synchronization problems of chaotic fuzzy cellular neural networks with time-varying delays. To overcome the difficulty that complete synchronization between non-identical chaotic neural networks cannot be achieved only by utilizing output feedback control, we use a sliding mode control approach to study the synchronization of non-identical chaotic fuzzy cellular neural networks with time-varying delays, where the parameters and activation functions are mismatched. This research demonstrates the effectiveness of application in secure communication. Numerical simulations are carried out to illustrate the main results.     

Delay-dependent exponential stability for a class of neural networks with time delays

This paper is concerned with the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type. In terms of a linear matrix inequality (LMI), a sufficient condition guaranteeing the existence, uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks is proposed. This condition is dependent on the size of the time delay, which is usually less conservative than delay-independent ones. The proposed LMI condition can be checked easily by recently developed algorithms solving LMIs. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.     

Stochastic exponential synchronization of jumping chaotic neural networks with mixed delays

This paper deals with the exponential synchronization problem for a class of stochastic jumping chaotic neural networks with mixed delays and sector bounded nonlinearities. The mixed time delays under consideration comprise both discrete time-varying delays and distributed time delays. By applying the Finsler’s Lemma and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent feedback controllers with sector nonlinearities are developed to achieve the synchronization in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve no free weighting matrices, the computational burden is largely reduced. One numerical example is provided to demonstrate the effectiveness of the theoretical results.     

混沌时滞随机神经网络同步控制

研究了一类混沌时滞随机神经网络同步控制问题．采用更具一般性的时滞反馈控制器,通过巧妙地构造Lyapunov数,分别得到了均方指数同步和均方渐近同步两个判别准则．仿真例子表明,新准则是有效的．     

Neural networks with discrete and distributed time-varying delays: A general stability analysis

In this paper, the global asymptotic and exponential stability are investigated for a class of neural networks with both the discrete and distributed time-varying delays. By using appropriate Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique, several delay-dependent sufficient conditions are obtained to guarantee the global asymptotic and exponential stability of the addressed neural networks. These conditions are expressed in terms of LMIs, and are dependent on both the discrete and distributed time delays. Therefore, the stability of the neural networks can be checked readily by resorting to the Matlab LMI toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the differentiability of the discrete and distributed time-varying delays, which means that our results generalize and further improve those in the earlier publications. A simulation example is given to show the effectiveness and less conservatism of the obtained conditions.     

Global exponential stability of static neural networks with delay and impulses: Discrete-time case

In this paper, we investigate the exponential stability of discrete-time static neural networks with impulses and variable time delay. The discrete-time neural networks are derived by discretizing the corresponding continuous-time counterparts with implicit-explicit-θ (IMEX-θ) method. The impulses are classified into three classes: input disturbances, stabilizing and “neutral” type— the impulses are neither helpful for stabilizing nor destabilizing the neural networks, and then by using a very excellent ideology introduced recently the connections between the impulses and the utilized Lyapunov function are fully explored with respect to each type of impulse. New analysis techniques that used to realize the ideology in discrete-time situation are proposed and it is shown that they are essentially different from the ones used in continuous-time case. Several criteria for global exponential stability of the static neural networks in discrete-time case are established in terms of linear matrix inequalities (LMIs) and numerical simulations are given to validate the obtained theoretical results.     

Robust exponential stability of Markovian jumping neural networks with mode-dependent delay

This paper deals with the robust exponential stability problem for a class of Markovian jumping neural networks with time delay. The delay considered varies randomly, depending on the mode of the networks. By using a new Lyapunov–Krasovskii functional, a delay-dependent stability criterion is presented, which can be expressed in terms of linear matrix inequalities (LMIs). A numerical example is given to show the effectiveness of the results.     

Exponential stability for stochastic BAM networks with discrete and distributed delays

In this paper, we investigate exponential stability for stochastic BAM networks with mixed delays. The mixed delays include discrete and distributed time-delays. The purpose of this paper is to establish some criteria to ensure the delayed stochastic BAM neural networks are exponential stable in the mean square. A sufficient condition is established by consructing suitable Lyapunov functionals. The condition is expressed in terms of the feasibility to a couple LMIs. Therefore, the exponential stability of the stochastic BAM networks with discrete and distributed delays can be easily checked by using the numerically efficient Matlab LMI toobox. A simple example is given to demonstrate the usefulness of the derived LMI-based stability conditions.