不确定离散时滞中立神经网络鲁棒稳定性分析

针对一类具有离散时滞和参数范数有界的不确定性中立神经网络的全局渐近鲁棒稳定性问题,通过应用范数和矩阵不等式分析方法,构造合适的Lyapunov-Krasovskii泛函,得到了新的与时滞无关的稳定性充分条件。该条件能够保证离散时滞中立神经网络在平衡点全局渐近鲁棒稳定。与现有文献中大多数LMI形式的稳定性准则不同,该稳定性判定准则中未知参数少且计算复杂度低,易于计算验证。最后,一个仿真算例验证了结论的有效性。     

中立联想记忆神经网络鲁棒稳定性新准则

针对一类具有离散时滞和参数范数有界的不确定性中立联想记忆神经网络的全局渐近鲁棒稳定性问题进行了研究.通过应用范数理论和矩阵不等式分析方法,并构造合适的Lyapunov-Krasovskii泛函,推导出了与时滞无关的新稳定性判定准则,用于保证神经网络的平衡点是全局渐近鲁棒稳定的.该准则中包含的未知参数少、计算复杂度低,易于验证.仿真算例验证了新判定准则的有效性.     

具有时变时滞的递归神经网络的渐近稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间.研究了带时变时滞的递归神经网络的全局渐近稳定性.首先将要研究的模型转化为描述系统模型,然后利用Lyapunov-Krasovskii稳定性定理、线性矩阵不等式(LMI)技术、S过程和代数不等式方法,得到了确保时变时滞递归神经网络渐近稳定性的新的充分条件,并将它应用于常时滞神经网络和时滞细胞神经网络模型,分别得到了相应的全局渐近稳定性条件.理论分析和数值模拟显示,所得结果为时滞递归神经网络提供了新的稳定性判定准则.     

关于线性中立型时滞系统稳定性代数准则的一个注记

研究了线性时滞中立型微分系统的渐近稳定性, 基于系统的特征方程, 利用恰当的模矩阵、谱半径和矩阵乘法公式导出了新的时滞无关的稳定性准则, 例子表明所给准则的有效性和较低的保守性.     

一类时变时滞中立微分方程的时滞相关稳定性判据

针对一类时变时滞中立型微分方程,利用Lyapunov--Krasovskii泛函方法,并结合线性矩阵不等式技巧,给出系统基于线性矩阵不等式（LMI）的全局渐近稳定的时滞相关充分条件,并通过算例与现有准则相比,本文所给条件是有效的具有较小的保守性。     

一类含有时变时滞的不确定中立型Hopfield神经网络的鲁棒稳定性判据

针对一类不确定中立型时变时滞Hopfield神经网络的鲁棒稳定性问题, 构造了一个新Lyapunov-Krasovskii泛函, 并结合自由矩阵方法和牛顿—莱布尼茨公式, 得到了新的时滞相关稳定性判据. 该判据考虑了中立型时变时滞Hopfield神经网络中的参数不确定性, 所得结果以线性矩阵不等式(Linear matrix inequality, LMI)的形式给出, 容易验证. 最后, 通过两个数值算例验证了该结果的有效性及可行性. 该判据对丰富与完善中立型神经网络的稳定性理论体系, 具有积极的意义.     

带区间时变时滞的BAM神经网络渐近稳定性

针对一类具有区间时滞和随机干扰的BAM神经网络的全局渐近稳定性问题,通过构造合适的Lyapunov-Krasovskii泛函,应用随机分析和自由权值矩阵方法,并考虑时滞区间范围,得到了新的稳定性充分条件。该条件能够保证时滞BAM神经网络在均方意义下是全局渐近稳定的,同时适用于快时滞和慢时滞,其适用范围更广。最后,通过一个仿真实例证明了定理的有效性。     

带区间时变时滞的BAM神经网络渐近稳定性

针对一类具有区间时滞和随机干扰的BAM神经网络的全局渐近稳定性问题,通过构造合适的Lyapunov-Krasovskii泛函,应用随机分析和自由权值矩阵方法,并考虑时滞区间范围,得到了新的稳定性充分条件。该条件能够保证时滞BAM神经网络在均方意义下是全局渐近稳定的,同时适用于快时滞和慢时滞,其适用范围更广。最后,通过一个仿真实例证明了定理的有效性。     

一类不确定中立型系统的时滞相关稳定准则

本文讨论了一类定常系数时变时滞中立型系统的时滞相关稳定性. 以线性矩阵不等式形式给出了新的时滞相关渐近稳定标准. 二个数值例子表明本文结果比先前结论有较小的保守性.     

基于 M 矩阵理论的时滞细胞神经网络稳定性分析*

研究了时滞细胞神经网络的稳定性问题。通过M‐矩阵理论及其判定引理,运用适当的线性参数变换,推导出时滞细胞神经网络的稳定性条件,相比常用的Lyapunov方法,论文为研究多时滞细胞神经网络的稳定性提供了一个更为简单的新方法,降低了原有结论的保守性,进一步推导完善了全局渐近稳定平衡点为原点时的充分条件。仿真实例证明了文章提供的方法有效可行。     

Global asymptotic stability of high-order Hopfield type neural networks with time delays

This paper studies the problem of global asymptotic stability of a class of high-order Hopfield type neural networks with time delays. By utilizing Lyapunov functionals, we obtain some sufficient conditions for the global asymptotic stability of the equilibrium point of such neural networks in terms of linear matrix inequality (LMI). Numerical examples are given to illustrate the advantages of our approach.     

Delay-dependent stability analysis for impulsive neural networks with time varying delays

In this paper, the global exponential stability and global asymptotic stability of the neural networks with impulsive effect and time varying delays is investigated. By using Lyapunov–Krasovskii-type functional, the quality of negative definite matrix and Cauchy criterion, we obtain the sufficient conditions for global exponential stability and global asymptotic stability of such model, in terms of linear matrix inequality (LMI), which depend on the delays. Two examples are given to illustrate the effectiveness of our theoretical results.     

Asymptotic Stability of Cohen–Grossberg BAM Neutral Type Neural Networks with Distributed Time Varying Delays

This paper is concerned with the problem of asymptotic stability of neutral type Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov–Krasovskii functional (LKF), reciprocal convex technique and Jensen’s inequality are used to delay-dependent conditions are established to analysis the asymptotic stability of Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. These stability conditions are formulated as linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. Finally numerical examples are given to illustrate the usefulness of our proposed method.     

Global asymptotic stability of recurrent neural networks with multiple time-varying delays.

In this paper, several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time-varying delays. The Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach are employed in our investigation. The results are shown to be generalizations of some previously published results and are less conservative than existing results. The present results are also applied to recurrent neural networks with constant time delays.     

Global asymptotic stability of neural networks with transmission delays

The problem of stability of the equilibrium of a class of neural networks with transmission delays is studied using the Lyapunov functional method and combining with the method of inequality analysis. Some sufficient conditions for global asymptotic stability of neural networks with transmission delays, which do not require symmetry of the connection matrix and nonlinear properties for neural units to be continuously differentiable or strictly monotonic increasing, are obtained. These conditions can be used to design globally stable networks and thus have important significance in both theory and applications. In addition, we give some examples to illustrate the main results.     

Existence and global asymptotic stability of periodic solution for discrete and distributed time-varying delayed neural networks with discontinuous activations

In this paper, we study a general class of neural networks with discrete and distributed time-varying delays, whose neuron activations are discontinuous and may be unbounded or nonmonotonic. By using the Leray-Schauder alternative theorem in multivalued analysis, matrix theory and generalized Lyapunov-like approach, we obtain some sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the periodic solution. Moreover, when all the variable coefficients and time delays are real constants, we discuss the global convergence in finite time of the neural network dynamical system. Our results extend previous works not only on discrete and distributed time-varying delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete and distributed time-varying delayed neural networks with discontinuous activations. Two numerical examples are given to illustrate the effectiveness of our main results.     

On Global Stability of Delayed BAM Stochastic Neural Networks with Markovian Switching

In this paper, the stability analysis problem is investigated for stochastic bi-directional associative memory (BAM) neural networks with Markovian jumping parameters and mixed time delays. Both the global asymptotic stability and global exponential stability are dealt with. The mixed time delays consist of both the discrete delays and the distributed delays. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, we employ the Lyapunov–Krasovskii stability theory and the Itô differential rule to establish sufficient conditions for the delayed BAM networks to be stochastically globally exponentially stable and stochastically globally asymptotically stable, respectively. These conditions are expressed in terms of the feasibility to a set of linear matrix inequalities (LMIs). Therefore, the global stability of the delayed BAM with Markovian jumping parameters can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions.     

The globally asymptotic stability analysis for a class of recurrent neural networks with delays

This paper considers the problem of global stability of neural networks with delays. By combining Lie algebra and the Lyapunov function with the integral inequality technique, we analyze the globally asymptotic stability of a class of recurrent neural networks with delays and give an estimate of the exponential stability. A few new sufficient conditions and criteria are proposed to ensure globally asymptotic stability of the equilibrium point of the neural networks. A few simulation examples are presented to demonstrate the effectiveness of the results and to improve feasibility.     

Global asymptotic stability analysis for neutral-type complex-valued neural networks with random time-varying delays

This paper investigates the global asymptotic stability problem for a class of neutral-type complex-valued neural networks with random time-varying delays. By introducing a stochastic variable with Bernoulli distribution, the information of time-varying delay is assumed to be random time-varying delays. By constructing an appropriate Lyapunov–Krasovskii functional and employing inequality technique, several sufficient conditions are obtained to ensure the global asymptotically stability of equilibrium point for the considered neural networks. The obtained stability criterion is expressed in terms of complex-valued linear matrix inequalities, which can be simply solved by effective YALMIP toolbox in MATLAB. Finally, three numerical examples are given to demonstrate the efficiency of the proposed main results.     

Globally asymptotic stability of a class of neutral-type neural networks with delays.

Several stability conditions for a class of systems with retarded-type delays are presented in the literature. However, no results have yet been presented for neural networks with neutral-type delays. Accordingly, this correspondence investigates the globally asymptotic stability of a class of neutral-type neural networks with delays. This class of systems includes Hopfield neural networks, cellular neural networks, and Cohen-Grossberg neural networks. Based on the Lyapunov stability method, two delay-independent sufficient stability conditions are derived. These stability conditions are easily checked and can be derived from the connection matrix and the network parameters without the requirement for any assumptions regarding the symmetry of the interconnections. Two illustrative examples are presented to demonstrate the validity of the proposed stability criteria.