Delay-Dependent Exponential Stability of Neural Networks With Variable Delay: An LMI Approach

This brief focuses on the problem of delay-dependent stability analysis of neural networks with variable delay. Two types of variable delay are considered: one is differentiable and has bounded derivative; the other one is continuous and may vary very fast. By introducing a new type of Lyapunov–Krasovskii functional, new delay-dependent sufficient conditions for exponential stability of delayed neural networks are derived in terms of linear matrix inequalities. We also obtain delay-independent stability criteria. Two examples are presented which show our results are less conservative than the existing stability criteria.     

具有时滞的高阶Hopfield型神经网络的稳定性

通过Lyapunov泛函的方法，对具有时滞的高阶连续型Hopfield神经网络平衡点的稳定性进行分析，利用Razumikhin定理得到平衡点全局一致渐近稳定的时滞相关与时滞无关充分条件。     

Global asymptotic stability of delayed Cohen-Grossberg neural networks

In this paper, we study the Cohen-Grossberg neural networks with discrete and distributed delays. For a general class of internal decay functions, without assuming the boundedness, differentiability, and monotonicity of the activation functions, we establish some sufficient conditions for the existence of a unique equilibrium and its global asymptotic stability. Theory of M-matrices and Lyapunov functional technique are employed. The criteria are independent of delays and hence delays are harmless in our case. Our results improve and generalize some existing ones.     

Global asymptotic stability and global exponential stability of delayed cellular neural networks

In this brief, many novel theorems and corollaries are presented regarding the global asymptotic stability and global exponential stability of cellular neural networks with constant and variable time delays. The stability conditions in the new results improve and generalize existing ones. Several examples are discussed to compare the new results with the existing ones.     

Global asymptotic stability and global exponential stability of neural networks with unbounded time-varying delays

This brief studies the global asymptotic stability and the global exponential stability of neural networks with unbounded time-varying delays and with bounded and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks are derived. The new results given in the brief extend the existing relevant stability results in the literature to cover more general neural networks.     

Global robust stability analysis of neural networks with multiple time delays

Global robust convergence properties of continuous-time neural networks with discrete delays are studied. By employing suitable Lyapunov functionals, we derive a set of delay-independent sufficient conditions for the existence, uniqueness, and global robust asymptotic stability of the equilibrium point. The conditions can be easily verified as they can be expressed in terms of the network parameters only. Some numerical examples are given to compare our results with previous robust stability results derived in the literature. One of our main results is shown to improve and generalize a previously published result. Other results proved to establish a new set of robust stability criteria for delayed neural networks.     

An analysis of global asymptotic stability of delayed Cohen-Grossberg neural networks via nonsmooth analysis

In this paper, using a method based on nonsmooth analysis and the Lyapunov method, several new sufficient conditions are derived to ensure existence and global asymptotic stability of the equilibrium point for delayed Cohen-Grossberg neural networks. The obtained criteria can be checked easily in practice and have a distinguished feature from previous studies, and our results do not need the smoothness of the behaved function, boundedness of the activation function and the symmetry of the connection matrices. Moreover, two examples are exploited to illustrate the effectiveness of the proposed criteria in comparison with some existing results.     

Novel Delay-Dependent Stability Results for Neural Networks with Time-Varying Delays

This paper is concerned with the stability of static neural networks with time-varying delays. With the construction of a new Lyapunov functional and advanced techniques for calculating its derivative, a delay-dependent stability criterion is obtained that is less conservative than existing ones. A delay-independent criterion is also given that, together with the delay-dependent one, can be checked using recently developed algorithms. Examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed results.     

Mean Square Exponential Stability for Uncertain Delayed Stochastic Neural Networks with Markovian Jump Parameters

This paper is concerned with the problem of delay-dependent mean square exponential stability for a class of delayed stochastic Hopfield neural networks with Markovian jump parameters. The delays here are time-varying delays. Based on a new Lyapunov–Krasovskii functional, delay-dependent stability conditions are derived by means of linear matrix inequalities (LMIs). It is shown that the proposed results can contain some existing stability conditions as a special case. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method, and the simulations show that our results are less conservative than the existing ones.     

Delay-Dependent Globally Exponential Stability Criteria for Static Neural Networks: An LMI Approach

The problem of globally exponential stability of static neural networks is investigated. Based on the Lyapunov-Krasovskii functional approach, the free-weighting matrix method, and the Jensen integral inequality, new delay-dependent stability criteria of the unique equilibrium of static neural networks with time-varying delays are presented in terms of linear matrix inequalities (LMIs). The stability criteria can easily be checked by using recently developed algorithms in solving LMIs. A numerical example is given to illustrate the effectiveness and less conservativeness of our proposed method.     

New Asymptotic Stability Criteria for a Two-Neuron Network With Different Time Delays

We present new sufficient conditions for the asymptotic stability of a two-neuron network with different time delays. These conditions lead to delay-dependent and delay-independent asymptotic stabilities, respectively. They are shown to be less conservative and restrictive than those reported in the literature. Some examples are included to illustrate our results.     

具反应扩散项变时滞细胞神经网络模型 指数稳定性的新结果

针对一类具反应扩散项的变时滞细胞神经网络模型,利用Poincare不等式与Hanalay不等式等知识,获得了该系统的指数稳定性条件,该稳定性条件包含了扩散算子项,与以往结果比较,获得的指数稳定性条件更强,且降低了已有结论的保守性.最后,通过实例说明该方法的有效性.     

基于LMI的时变时滞Cohen-Grossberg神经网络鲁棒稳定性

 研究了时变时滞Cohen-Grossberg神经网络的全局鲁棒稳定性问题.基于线性矩阵不等式技术,给出了保证时变时滞Cohen-Grossberg神经网络平衡点唯一性和全局鲁棒稳定性的新判据.这些新判据不依赖于时滞的大小和放大函数,且与现有的一些结果相比,具有易于验证、适用范围广、条件更不保守等特点.仿真结果验证了本文方法的有效性.     

Robust Adaptive Control of Unknown Modified Cohen–Grossberg Neural Networks With Delays

In this brief, robust adaptive control of unknown modified Cohen-Grossberg neural networks with time delays is considered based on nonsmooth analysis and matrix inequality technique. Several new controllers are designed to ensure the global asymptotical stability of the targeted equilibrium point. The designed controllers are independent of the bounds of the perturbations, system functions and the time delays. One does not need to know the bounds of the unknown parameters, but only needs to know the structures of the modified Cohen-Grossberg neural networks with time delays. Finally, some simulations examples are given to verify the theoretical results.     

一类时变时滞模糊细胞神经网络的 时滞依赖指数稳定性判据

 针对一类带有时变时滞的模糊细胞神经网络,通过适当的构造Lyapunov-Krasovskii泛函,以线性矩阵不等式的形式提出了一种新颖的依赖于时滞的全局指数稳定性判据.与之前结果相比,所提出的判据针对模糊时滞项进行了变换,从而首次考虑了模糊细胞神经网络中非模糊项的连接权矩阵中元素的符号问题,降低了判据的保守性.并且时滞变化率的限制将被放松.仿真结果进一步证明了判据的有效性.     

Global exponential stability and periodicity of recurrent neural networks with time delays

In this paper, the global exponential stability and periodicity of a class of recurrent neural networks with time delays are addressed by using Lyapunov functional method and inequality techniques. The delayed neural network includes the well-known Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks as its special cases. New criteria are found to ascertain the global exponential stability and periodicity of the recurrent neural networks with time delays, and are also shown to be different from and improve upon existing ones.     

Global convergence of Lotka-Volterra recurrent neural networks with delays

Recurrent neural networks of the Lotka-Volterra model have been proven to possess characteristics which are desirable in some neural computations. A clear understanding of the dynamical properties of a recurrent neural network is necessary for efficient applications of the network. This paper studies the global convergence of general Lotka-Volterra recurrent neural networks with variable delays. The contributions of this paper are: 1) sufficient conditions are established for lower positive boundedness of the networks; 2) global exponential stability conditions are obtained for the networks. These conditions are totally independent of the variable delays which are therefore allowed to be uncertain; 3) novel Lyapunov functionals are constructed to establish delays dependent conditions for global asymptotic stability, and 4) simulation results and examples are provided to supplement and illustrate the theoretical contributions presented.     

Delay-Dependent Exponential Stability for Uncertain Stochastic Hopfield Neural Networks With Time-Varying Delays

This paper provides new delay-dependent conditions that guarantee the robust exponential stability of stochastic Hopfield type neural networks with time-varying delays and parameter uncertainties. Both the cases of the time-varying delays which are differentiable and may not be differentiable are considered. The stability conditions are derived by using the recently developed free-weighting matrices technique and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria. It is shown that the proposed stability results are less conservative than some previous ones in the literature.      

Novel Delay-Dependent Stability Criteria for Fuzzy Neural Networks Using Delay-Decomposition Approach

This paper investigates the global asymptotic stability of fuzzy neural networks with time-varying and unbounded continuously distributed delays in mean square. Based on a new Lyapunov–Krasovskii functional, by effective combination of Jensen integral inequality with reciprocally convex and quadratic convex combination method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which are expressed in terms of linear matrix inequalities, can be easily verified via MATLAB software. The main advantage of the proposed criteria lies in its reduced conservatism by means of the time delay-decomposition technique and Wirtinger-based inequality. In addition to that, a numerical example is given to demonstrate the effectiveness and less conservativeness of our theoretical results over the existing literature.     

随机变时滞神经网络的全局渐近稳定性

研究了一类具有变时滞随机神经网络模型平衡点的全局渐近稳定性问题,通过构造李亚普诺夫函数并利用线性矩阵不等式理论,得出了随机变时滞神经网络的全局渐近稳定性的充分条件。