非线性随机时滞系统族的鲁棒稳定性

研究了不确定性的一族非线性随机时滞系统的指数稳定性,建立了这种系统的均 方指数稳定和几乎必然指数稳定的时滞相关的充分准则;然后应用这些充分条件到一类不确 定性的随机时滞神经网络,得到了这种神经网络指数稳定的实用判据.最后一个数值例子说 明所给准则的有效性.     

随机混沌时滞神经网络的指数同步

研究受随机扰动且具有时变时滞神经网络的指数同步. 根据Lyapunov稳定性理论结合线性矩阵不等式技巧, 通过构造含时滞的状态反馈控制器, 使得受到随机扰动的驱动系统和响应系统达到指数同步, 给出了随机时滞神经网络指数同步的新判据, 最后通过仿真验证了所用方法的有效性.     

带有时滞的随机区间Hopfield神经网络的指数稳定性

讨论了带有可变时滞的随机区间Hopfield神经网络的指数稳定性, 利用It^o公式和Lyapunov函数, 得到了几个关于其指数稳定时滞无关和时滞相关的充分性条件, 推广了现有文献中关于定常时滞随机神经网络及其确定形式的许多结果.     

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.     

随机时滞神经网络的全局指数稳定性

首先对一般随机系统的渐近特性进行了讨论.然后结合神经网络的特点,应用李雅普诺夫第二方法对一类随机时滞神经网络系统的全局指数稳定性进行了分析,给出了易于判定随机时滞神经网络几乎必然指数稳定性新的代数判据,并给出实例进行仿真实验.     

基于LMI方法的时滞细胞神经网络稳定性分析

神经网络是一个复杂的大规模非线性系统，而时滞神经网络的动态行为更为丰富和复杂．现有的研究时滞神经网络稳定性的方法中最为流行的是Lyapunov方法．它把稳定性问题变为某些适当地定义在系统轨迹上的泛函，通过这些泛函相应的稳定性条件就可以获得．该文得到了时滞细胞神经网络渐近稳定性的一些充分条件．作者利用了泛函微分方程的Lyapunov—Krasovskii稳定性理论和线性矩阵不等式(LMI)方法，精炼和推广了一些已有的结果．它们比目前文献报道的结果更少保守．该文还给出了确定时滞细胞神经网络稳定性更多的判定准则．     

不确定切换奇异时滞系统鲁棒指数容许性分析

讨论一类连续时间不确定切换奇异区间时变时滞系统的鲁棒指数容许性问题. 通过定义衰减率依赖李亚普诺夫函数并利用平均驻留时间法, 给出一个时滞区间依赖充分条件保证标称系统正则、无脉冲且均方指数稳定. 同时该准则也被推广至不确定系统. 本文获得的结论为连续时间切换奇异时滞系统的基本问题提供了一个解, 即识别切换信号使得切换奇异时滞系统正则、无脉冲且均方指数稳定. 数值例子说明本文结果的有效性.     

脉冲时滞Hopfield神经网络的全局指数稳定性

研究一类具有脉冲控制的时滞Hopfideld神经网络的全局指数稳定性,通过Lyapunov-Krasovskii稳定性理论和Halanay不等式等方法,构造合适的Lyapunov泛函,利用不等式技巧得到了确保时滞神经网络在脉冲控制下全局指数稳定的一个充分条件,保证了Hofidd神经网络在脉冲控制下的全局指数稳定,并估计了系统的指数收敛率.为了便于计算和验证结论的有效性,给出一个简化的充分条件.最后通过数值实例的实验仿真证实了结论的有效性、可行性.     

具有时滞脉冲的线性随机时滞系统的均方指数稳定

本文研究了具有时滞脉冲的线性随机时滞系统的稳定性问题,基于Lyapunov函数和Razumikhin技巧,针对具有镇定型脉冲和反镇定型脉冲的线性随机时滞系统分别建立了系统均方指数稳定的充分条件,最后给出两个数值例子论证结果的有效性.     

不确定广义跳变时滞系统的鲁棒指数稳定性

讨论不确定广义跳变时滞系统的鲁棒指数稳定性问题. 利用线性矩阵不等式(LMI)技术给出一个时滞区间依赖条件保证标称系统正则、无脉冲且均方指数稳定. 同时该准则也被推广至不确定系统. 数值例子说明本文的结果改进了已有的结论.     

Exponential ultimate boundedness of impulsive stochastic delay difference systems

This paper is concerned with the exponential ultimate boundedness problems for the impulsive stochastic delay difference systems. Several sufficient conditions on the global pth moment exponential ultimate boundedness are presented by using the Lyapunov methods and the algebraic inequality techniques, and the estimated exponential convergence rate and the ultimate bound are provided as well. As an application, the boundedness criteria are applied to a class of discrete impulsive stochastic neural networks with delays. The obtained results show that the impulses not only can stabilize an unstable stochastic difference delay system but also can make an unbounded stochastic difference delay system into a bounded system. Examples and simulations are also provided to demonstrate the effectiveness of the derived theoretical results.     

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.     

时滞非线性随机大系统的指数稳定性

建立了一般随机泛函微分方程p阶均值指数稳定与几乎必然指数稳定的新型判据, 然后应用所得判据到具有可变多时滞的非线性随机大系统, 得到了这种随机大系统时滞无关的均方指数稳定与几乎必然指数稳定的代数判据.     

Exponential stability of switched stochastic delay systems with non-linear uncertainties

This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are derived in terms of linear matrix inequalities and average dwell-time conditions. Numerical examples are also given to illustrate the results.     

Analysis of linear asynchronous hybrid stochastic systems and its application to multi-agent systems with Markovian switching topologies

This paper studies the stability and stabilisation of a class of asynchronous hybrid stochastic systems described by linear Markov jump systems with asynchronous parameters induced by hysteretic mode and input delay. By exploring the essential properties of the Markov chain and developing novel Lyapunov function/functional based approaches, we derive sufficient conditions in terms of sizes of the delays ensuring the mean square asymptotical stability of the systems. Interestingly, the Lyapunov functional based approach further leads to the mean square stability criteria that depend only on the drift part and allow an arbitrary large delay for the diffusion part, which is different from the Lyapunov-Razumikhin based results. The theoretical results are applied to solve the consensus problems of multi-agent systems with Markovian switching topologies and input delay. Numerical examples demonstrate the established results.     

Robust Exponential Stability and Stabilization of a Class of Nonlinear Stochastic Time‐Delay Systems

This paper presents new exponential stability and delayed‐state‐feedback stabilization criteria for a class of nonlinear uncertain stochastic time‐delay systems. By choosing the delay fraction number as two, applying the Jensen inequality to every sub‐interval of the time delay interval and avoiding using any free weighting matrix, the method proposed can reduce the computational complexity and conservativeness of results. Based on Lyapunov stability theory, exponential stability and delayed‐state‐feedback stabilization conditions of nonlinear uncertain stochastic systems with the state delay are obtained. In the sequence, the delayed‐state‐feedback stabilization problem for a nonlinear uncertain stochastic time‐delay system is investigated and some sufficient conditions are given in the form of nonlinear inequalities. In order to solve the nonlinear problem, a cone complementarity linearization algorithm is offered. Mathematical and/or numerical comparisons between the proposed method and existing ones are demonstrated, which show the effectiveness and less conservativeness of the proposed method.     

具有非线性滞后关联的随机大系统的分散镇定

本文通过利用李雅普诺夫函数和李雅普诺夫矩阵方程的性质，对具有非线性滞后关联的一类随机大系统建立了分散鲁棒镇定的判据，所得闭环随机大系统的和稳定性不依赖于任意实数滞后，并对不确定系数矩阵和随机扰动强度具有鲁棒性。