Stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks with mixed delays and the Wiener process based on sampled-data control

We investigate the stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks (MJFCNNs) with discrete, unbounded distributed delays, and the Wiener process based on sampled-data control using the linear matrix inequality (LMI) approach. The Lyapunov-Krasovskii functional combined with the input delay approach as well as the free-weighting matrix approach is employed to derive several sufficient criteria in terms of LMIs to ensure that the delayed MJFCNNs with the Wiener process is stochastic asymptotical synchronous. Restrictions (e.g., time derivative is smaller than one) are removed to obtain a proposed sampled-data controller. Finally, a numerical example is provided to demonstrate the reliability of the derived results.     

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.     

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.     

Robust lag synchronization between two different chaotic systems via dual-stage impulsive control

In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme (the so-called dual-stage impulsive control), some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.     

具有双重时滞的时变耦合复杂网络的牵制外同步研究

针对同时具有节点时滞和耦合时滞的时变耦合复杂网络的外同步问题, 提出一种简单有效的自适应牵制控制方法. 首先构建一种贴近实际的驱动-响应复杂网络模型, 在模型中引入双重时滞和时变不对称外部耦合矩阵. 进一步设计易于实现的自适应牵制控制器, 对网络中的一部分关键节点进行控制. 构造适当的Lyapunov泛函, 利用 LaSalle不变集原理和线性矩阵不等式, 给出两个复杂网络实现外同步的充分条件. 最后, 仿真结果表明所提同步方法的有效性, 同时揭示耦合时滞对同步收敛速度的影响.     

Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks

In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality (LMI) are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control algorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method.     

Non-fragile synchronization of genetic regulatory networks with randomly occurring controller gain fluctuation

This study examines the non-fragile synchronization of genetic regulatory networks (GRNs) with time-varying delays. Genetic regulatory network is formulated and sufficient conditions are derived to guarantee its synchronization based on master-slave system approach. The non-fragile observer based feedback controller gains are assumed to have the random fluctuations, two different types of uncertainties which perturb the gains are taken into account. By constructing a suitable Lyapunov-Krasovskii stability theory together with linear matrix inequality (LMI) approach we derived the delay-dependent criteria to ensure the asymptotic stability of the error system, which guarantees the master system synchronize with the slave system. The expressions for the non-fragile controller can be obtained by solving a set of LMIs using standard softwares. Finally, some numerical examples are included to show that the proposed method is less conservative than existing ones.     

Robust exponential stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters

This Letter is concerned with delay-dependent robust exponential mean square stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters. Time delays here are discrete and distributed time-varying delays. Based on Lyapunov-Krasovskii stability theory, delay-dependent stability conditions are derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

Stability and synchronization of fractional-order complex-valued neural networks with time delay: LMI approach

In this paper, we investigate the problem of stability and synchronization of fractional-order complex-valued neural networks with time delay. By using Lyapunov–Krasovskii functional approach, some linear matrix inequality (LMI) conditions are proposed to ensure that the equilibrium point of the addressed neural networks is globally Mittag–Leffler stable. Moreover, some sufficient conditions for projective synchronization of considered fractional-order complex-valued neural networks are derived in terms of LMIs. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results.     

Synchronization of delayed fuzzy cellular neural networks based on adaptive control

This Letter studies synchronization of delayed fuzzy cellular neural networks with all the parameters unknown. To enhance the coupled strength dynamically and be more suitable for the reality, we add fuzzy theory to the traditional cellular neural networks. By the Lyapunov-Lasall principle of functional differential equations, some new stability criteria are obtained via adaptive control. To the best of our knowledge, there has few work studying fuzzy cellular neural networks. Moreover, the approaches developed here extend the ideas and techniques derived in recent literatures. In the end, an example and its simulation were given to illustrate the simpleness and effectiveness of our main results.     

Exponential synchronization of complex networks with Markovian jump and mixed delays

In this Letter, we investigate the exponential synchronization problem for an array of N linearly coupled complex networks with Markovian jump and mixed time-delays. The complex network consists of m modes and the network switches from one mode to another according to a Markovian chain with known transition probability. The mixed time-delays are composed of discrete and distributed delays, both of which are mode-dependent. The nonlinearities imbedded with the complex networks are assumed to satisfy the sector condition that is more general than the commonly used Lipschitz condition. By making use of the Kronecker product and the stochastic analysis tool, we propose a novel Lyapunov–Krasovskii functional suitable for handling distributed delays and then show that the addressed synchronization problem is solvable if a set of linear matrix inequalities (LMIs) are feasible. Therefore, a unified LMI approach is developed to establish sufficient conditions for the coupled complex network to be globally exponentially synchronized in the mean square. Note that the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. A simulation example is provided to demonstrate the usefulness of the main results obtained.     

Stochastic synchronization of coupled neural networks with intermittent control

In this Letter, we study the exponential stochastic synchronization problem for coupled neural networks with stochastic noise perturbations. Based on Lyapunov stability theory, inequality techniques, the properties of Weiner process, and adding different intermittent controllers, several sufficient conditions are obtained to ensure exponential stochastic synchronization of coupled neural networks with or without coupling delays under stochastic perturbations. These stochastic synchronization criteria are expressed in terms of several lower-dimensional linear matrix inequalities (LMIs) and can be easily verified. Moreover, the results of this Letter are applicable to both directed and undirected weighted networks. A numerical example and its simulations are offered to show the effectiveness of our new 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.     

Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays

In this Letter, we have dealt with the problem of lag synchronization and parameter identification for a class of chaotic neural networks with stochastic perturbation, which involve both the discrete and distributed time-varying delays. By the adaptive feedback technique, several sufficient conditions have been derived to ensure the synchronization of stochastic chaotic neural networks. Moreover, all the connection weight matrices can be estimated while the lag synchronization is achieved in mean square at the same time. The corresponding simulation results are given to show the effectiveness of the proposed method.     

Periodically intermittent controlling complex dynamical networks with time-varying delays to a desired orbit

This Letter investigates the problem of synchronization in complex dynamical networks with time-varying delays. A periodically intermittent control scheme is proposed to achieve global exponential synchronization for a general complex network with both time-varying delays dynamical nodes and time-varying delays coupling. It is shown that the sates of the general complex network with both time-varying delays dynamical nodes and time-varying delays coupling can globally exponentially synchronize with a desired orbit under the designed intermittent controllers. Moreover, a typical network consisting of the time-delayed Chua oscillator with nearest-neighbor unidirectional time-varying delays coupling is given as an example to verify the effectiveness of the proposed control methodology.     

Global synchronization in general complex delayed dynamical networks and its applications

The main objective of the present paper is further to investigate global synchronization of a general model of complex delayed dynamical networks. Based on stability theory on delayed dynamical systems, some simple yet less conservative criteria for both delay-independent and delay-dependent global synchronization of the networks are derived analytically. It is shown that under some conditions, if the uncoupled dynamical node is stable itself, then the network can be globally synchronized for any coupling delays as long as the coupling strength is small enough. On the other hand, if each dynamical node of the network is chaotic, then global synchronization of the networks is heavily dependent on the effects of coupling delays in addition to the connection configuration. Furthermore, the results are applied to some typical small-world (SW) and scale-free (SF) complex networks composing of coupled dynamical nodes such as the cellular neural networks (CNNs) and the chaotic FHN neuron oscillators, and numerical simulations are given to verify and also visualize the theoretical results.     

基于自适应-脉冲控制方法实现时变耦合驱动-响应复杂网络的投影同步

最近,对时变延迟网络的脉冲稳定性的研究大量出现,但通过自适应-脉冲控制方法获得的时变延迟网络同步准则却很少.本文中,运用自适应-脉冲控制方法,设计自适应反馈控制器、自适应律和线性脉冲控制器,研究时变耦合部分线性系统驱动-响应复杂网络的投影同步.获得时变耦合网络的自适应-脉冲投影同步准则.并且不需要网络的耦合构造矩阵是不可约的.另外,运用数值模拟证实方案的有效性和可行性.     

A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov--Krasovskii functional

In this paper,new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived.The stability conditions are represented in terms of linear matrix inequalities(LMIs) by constructing new Lyapunov-Krasovskii functional.The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints.The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound.Numerical examples are presented to show the effectiveness of the proposed method.     

Novel global robust stability criteria for interval neural networks with multiple time-varying delays

This Letter is concerned with the problem of robust stability analysis for interval neural networks with multiple time-varying delays and parameter uncertainties. The parameter uncertainties are assumed to be bounded in given compact sets and the activation functions are supposed to be bounded and globally Lipschitz continuous. A sufficient condition is obtained by means of Lyapunov functionals, which guarantees the existence, uniqueness and global asymptotic stability of the delayed neural network for all admissible uncertainties. This condition is in terms of a linear matrix inequality (LMI), which can be easily checked by using recently developed algorithms in solving LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

Stability analysis of fractional order fuzzy cellular neural networks with leakage delay and time varying delays

In this paper we investigated the stability of fractional order fuzzy cellular neural networks with leakage delay and time varying delays. Based on Lyapunov theory and applying bounded techniques of fractional calculation, sufficient criterion are established to guarantee the stability. Hybrid feedback control is applied to derive the proposed results. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.