Stability analysis for coupled systems with time delay on networks

In this paper, the stability problem for some coupled systems with time delay on networks (CSDNs) is investigated. We provide a systematic method for constructing a global Lyapunov functional for CSDNs by using graph theory. The stability, uniform stability and global uniform stability of the systems are investigated. And by using the Lyapunov functional constructed, some sufficient conditions of stability are obtained.     

New asymptotic stability criteria for neural networks with time-varying delay

The problem of delay-dependent asymptotic stability criteria for neural networks with time-varying delay is investigated. A new class of Lyapunov functional is constructed to derive some new delay-dependent stability criteria.The obtained criterion are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.     

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

This paper studies the problem of linear matrix inequality (LMI) approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach,the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional,some inequality techniques and stochastic stability theory,new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism,which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally,numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.     

Improved stability criteria for neural networks with time-varying delay

The problem of the stability analysis of neural networks with time-varying delay is considered in this Letter. By constructing a new augmented Lyapunov functional which contains a triple-integral term, an improved delay-dependent stability criterion is derived in terms of LMI using the free-weighting matrices method. The rate-range of the delay is also considered in the derivation of the criterion. Numerical examples are presented to illustrate the effectiveness of the proposed method.     

时滞双向联想记忆神经网络的全局稳定性

通过构造一个合适的Lyapunov泛函及应用不等式的分析技巧研究了具有时滞的双向联想记忆 神经网络的平衡点的全局稳定性问题-在对神经元激励函数较宽松的假设条件下（可以不满 足Lipschitz条件），获得了一个新的保证全局渐近稳定性的判定准则-结果可应用于包含非 Lipschitz的一类更加广泛的神经元激励函数的神经网络的设计中- 关键词： Lyapunov泛函 时滞 双向联想记忆神经网络 全局渐近稳定性     

Global exponential stability for nonautonomous cellular neural networks with delays

In this Letter, by utilizing Lyapunov functional method and Halanay inequalities, we analyze global exponential stability of nonautonomous cellular neural networks with delay. Several new sufficient conditions ensuring global exponential stability of the network are obtained. The results given here extend and improve the earlier publications. An example is given to demonstrate the effectiveness of the obtained results.     

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.     

Successive lag synchronization on dynamical networks with communication delay

In this paper, successive lag synchronization(SLS) on a dynamical network with communication delay is investigated.In order to achieve SLS on the dynamical network with communication delay, we design linear feedback control and adaptive control, respectively. By using the Lyapunov function method, we obtain some sufficient conditions for global stability of SLS. To verify these results, some numerical examples are further presented. This work may find potential applications in consensus of multi-agent systems.     

Free-matrix-based time-dependent discontinuous Lyapunov functional for synchronization of delayed neural networks with sampled-data control

This paper is concerned with the synchronization of delayed neural networks via sampled-data control. A new technique, namely, the free-matrix-based time-dependent discontinuous Lyapunov functional approach, is adopted in constructing the Lyapunov functional, which takes advantage of the sampling characteristic of sawtooth input delay. Based on this discontinuous Lyapunov functional, some less conservative synchronization criteria are established to ensure that the slave system is synchronous with the master system. The desired sampled-data controller can be obtained through the use of the linear matrix inequality(LMI) technique. Finally, two numerical examples are provided to demonstrate the effectiveness and the improvements of the proposed methods.     

切换系统的异步镇定: 相邻模型依赖平均驻留时间

本文研究一类切换线性系统在异步切换下的镇定问题. 由于控制器的切换信号中存在时滞使得控制器的切换和系统的切换出现了异步的情况. 首先, 提出了相邻模型依赖平均驻留时间的定义. 然后, 通过合并切换信号的方法和多Lyapunov函数方法, 给出了相邻模型依赖平均驻留时间切换下整个切换系统稳定的充分条件和控制器设计. 这些条件反映了系统的连续动态、切换时滞和平均驻留时间之间的关系. 最后, 通过例子验证了本文方法的有效性.     

New results on global exponential stability of competitive neural networks with different time scales and time-varying delays

This paper studies the global exponential stability of competitive neural networks with different time scales and time-varying delays. By using the method of the proper Lyapunov functions and inequality technique, some sufficient conditions are presented for global exponential stability of delay competitive neural networks with different time scales. These conditions obtained have important leading significance in the designs and applications of global exponential stability for competitive neural networks. Finally, an example with its simulation is provided to demonstrate the usefulness of the proposed criteria.     

Dual-anticipating, dual and dual-lag synchronization in modulated time-delayed systems

In this Letter, dual synchronization in modulated time delay system using delay feedback controller is proposed. Based on Lyapunov stability theory, we suggest a general method to achieve the dual-anticipating, dual, dual-lag synchronization of time-delayed chaotic systems and we find both its existing and sufficient stability conditions. Numerically it is shown that the dual synchronization is also possible when driving system contain two completely different systems. Effect of parameter mismatch on dual synchronization is also discussed. As an example, numerical simulations for the Mackey-Glass and Ikeda systems are conducted, which is in good agreement with the theoretical analysis.     

Mean square exponential stability of uncertain stochastic delayed neural networks

This Letter concerns with the mean square exponential stability of uncertain stochastic delayed neural networks. By applying Lyapunov functional method, new delay-dependent/independent mean square exponential stability criteria are derived in terms of linear matrix inequalities. Two examples are presented which show our result are less conservative than the existing stability criteria.     

Novel criteria for exponential synchronization of inner time-varying complex networks with coupling delay

This paper mainly investigates the exponential synchronization of an inner time-varying complex network with coupling delay. Firstly, the synchronization of complex networks is decoupled into the stability of the corresponding dynamical systems. Based on the Lyapunov function theory, some sufficient conditions to guarantee its stability with any given convergence rate are derived, thus the synchronization of the networks is achieved. Finally, the results are illustrated by a simple time-varying network model with a coupling delay. All involved numerical simulations verify the correctness of the theoretical analysis.     

A delay-decomposition approach for stability of neural network with time-varying delay

This paper studies delay-dependent asymptotical stability problems for the neural system with time-varying delay. By dividing the whole interval into multiple segments such that each segment has a different Lyapunov matrix, some improved delay-dependent stability conditions are derived by employing an integral equality technique. A numerical example is given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Global exponential convergence analysis of delayed cellular neural networks

Some sufficient criteria have been established to ensure the global exponential stability of delayed cellular neural networks by using an approach based on delay differential inequality. Compared with the method of Lyapunov functionals as in most previous studies, our method is simpler and more effective for a stability analysis of delayed system. Some previously established results in the literature are shown to be special cases of the present result.     

Delay-Dependent Exponential Synchronization Criteria for Chaotic Neural Networks with Time-Varying Delays

The problem of exponentially synchronizing class of delayed neural networks is studied. Both constant and time-varying delays are considered, to obtain the delay-dependent state feedback synchronization gain matrix. By means of the method of Lyapunov–Krasovskii functional, combined with linear matrix inequalities, exponential synchronization of the master–slave structure of neural networks is achieved. The delay interval is decomposed into multiple nonequidistant subintervals, on which Lyapunov–Krasovskii functionals are constructed. On the basis of these functionals, a new exponential synchronization condition, one that is time-delay dependent, is proposed in terms of linear matrix inequalities. A numerical example showing the effectiveness of the proposed method is presented.     

Some theoretical and numerical results for delayed neural field equations

In this paper we study neural field models with delays which define a useful framework for modeling macroscopic parts of the cortex involving several populations of neurons. Nonlinear delayed integro-differential equations describe the spatio-temporal behavior of these fields. Using methods from the theory of delay differential equations, we show the existence and uniqueness of a solution of these equations. A Lyapunov analysis gives us sufficient conditions for the solutions to be asymptotically stable. We also present a fairly detailed study of the numerical computation of these solutions. This is, to our knowledge, the first time that a serious analysis of the problem of the existence and uniqueness of a solution of these equations has been performed. Another original contribution of ours is the definition of a Lyapunov functional and the result of stability it implies. We illustrate our numerical schemes on a variety of examples that are relevant to modeling in neuroscience.     

Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification

In this paper, the adaptive synchronization and lag synchronization are considered for uncertain dynamical system with time delay based on parameter identification and a novel control method is then further given using the Lyapunov functional method. With this new and effective method, parameter identification and lag synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis in this paper.     

Existence and Nonlinear Stability of Stationary States of the Schrödinger–Poisson System

We consider the Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. Given a stationary state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such states we start with a given Casimir functional and construct a new functional which is in some sense dual to the corresponding energy-Casimir functional. This dual functional has a unique maximizer which is a stationary state of the Schrödinger–Poisson system and lies in the stability class. The stationary states are parameterized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels.