广义相对Dalquist数及其在非线性系统稳定性分析中的应用

对非线性算子引入了一个新概念——广义相对Dalquist数,建立了一般的非线性系统稳定性分析的一种新方法.借助这一新方法,得到了非线性系统指数稳定的充分条件,并给出了解的指数衰减估计.     

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考察一类Markov切换时变时滞随机系统的均方指数稳定性. 利用基于Liapunov函数和线性矩阵不等式的方法, 给出了使状态反馈控制系统能克服不确定性和随机干扰, 在均方意义下达到指数稳定的充分条件. 当Markov链遍历所有模态时, 给出了一个独立于Markov链模态集的增益矩阵, 使得状态反馈控制系统均方指数稳定     

广义系统渐近稳定性的一种新的Lyapunov判别方法

本文中，对广义系统构造了一种新的Lyapunov函数，并给出相应的渐近稳定性的Laypunov判别方法。另外，我们证明了当广义系数为R－能稳时，必存在一反馈控制使得闭环系统为渐近稳定性的。     

广义对角多项式指数和的估计

利用高斯和与次数矩阵Smith标准形的不变因子,给出了有限域上广义对角多项式指数和的估计,从而改进了Deligne-Weil型估计这类多项式指数和的结果.     

一类非线性不确定系统的全局指数镇定

研究一类非线性不确定系统的全局指数镇定问题.提出了连续反馈控制器的设计方法,并给出一类非线性不确定系统全局指数镇定的充分条件.如果充分条件得到满足,证明了提出的连续反馈控制使得闭环系统是全局指数稳定的.实例表明了所得结果的有效性.     

Cohen-Grossberg神经网络指数稳定性的新判则

避免构造Lyapunov函数的困难,运用广义Dahlquist数方法研究了Cohen- Grossberg神经网络模型的指数稳定性,不但得到了Cohen-Grossberg神经网络平衡点存在惟一性和指数稳定性的全新充分条件,而且给出了神经网络的指数衰减估计.与已有文献结果相比,所得的神经网络指数稳定的充分条件更为宽松,给出的解的指数衰减速度估计也更为精确.     

一类不确定广义周期时变系统的鲁棒H_∞控制

本文研究了状态矩阵具不确定性广义周期时变系统的鲁棒H∞控制问题.利用线性矩阵不等式(LMI)方法,在给出不确定广义周期时变系统广义可镇定和广义二次可镇定且具有H∞性能指标概念的基础上,得到了该系统广义二次可镇定且具有H∞性能指标γ的充要条件,并给出了相应的鲁棒H∞状态反馈控制律的设计方法,推广了周期系统的鲁棒控制理论结果.最后,通过数值算例说明了设计方法的有效性.     

二维粘弹性问题的广义差分法及其数值模拟

本文利用广义差分法讨论了二维粘弹性问题.建立了二维粘弹性问题的广义差分格式,给出了一种新的初始值近似,证明了广义差分解的最优L~p估计和W~1,p(2≤p≤∞)模估计,同时得到了广义的Ritz—Volterra投影和广义差分解之间的超收敛的W~1,p(2≤p≤∞)模的误差估计.最后给出了一个数值算例以验证该方法的可行性.     

统一混沌系统的全局指数吸引集的新结果

研究了参数α∈[1/29,14/173)时,统一混沌系统的全局指数吸引集问题.通过线性变换和广义Lyapunov函数方法,给出了系统最终上界的精确估计.所得结果发展和丰富了现有混沌系统吸引集的结果,并将在混沌控制和同步中得到广泛应用.     

参数不确定性广义周期时变系统的鲁棒H_∞控制

研究状态矩阵和控制输入矩阵均具不确定性广义周期时变系统的鲁棒H_∞控制问题.提出参数不确定性广义周期时变系统广义可镇定和广义二次可镇定且具有H_∞性能指标的概念,利用线性矩阵不等式(LMI)方法,得到了参数不确定性广义周期时变系统广义二次可镇定且具有H_∞性能指标γ的充要条件,给出了相应的鲁棒H_∞状态反馈控制律的设计方法.最后,通过数值算例说明了设计方法的有效性.     

Dynamical behaviors of a new hyperchaotic system

Currently, chaotic systems and chaos‐based applications are commonly used in the engineering fields. One of the main structures used in these applications is chaotic control and synchronization. In this paper, the dynamical behaviors of a new hyperchaotic system are considered. Based on Lyapunov Theorem with differential and integral inequalities, the global exponential attractive sets and positively invariant sets are obtained. Furthermore, the rate of the trajectories is also obtained. The global exponential attractive sets of the system obtained in this paper also offer theoretical support to study chaotic control, chaotic synchronization for this system. Computer simulation results show that the proposed method is effective. Copyright © 2014 John Wiley & Sons, Ltd.     

非自治变时滞Cohen-Grossberg网络的Lagrange稳定性和全局指数吸引集

基于考虑两种不同类型的激活函数,本文研究了非自治变时滞Cohen-Grossberg神经网络（CGNN）在Lagrange意义下的全局指数稳定性,通过利用新的不等式技巧和构造恰当的Lyapunov泛函给出非自治变时滞CGNN模型在Lagrange意义下全局指数稳定性（即一致有界性）以及对其全局指数吸引集估计的代数判据,并给出应用例子加以验证.     

Positive invariant sets and global exponential attractive sets of a class of neural networks with unbounded time-delays

In this paper, we study the positive invariant sets and global exponential attractive sets for a class of neural networks with unbounded time-delays. Based on the assumption for the activation function satisfying the global Lipschitz condition, several algebraic criterions for the aforementioned sets are obtained by constructing proper Lyapunov functions and employing Young inequality. Finally, examples are given and analyzed to demonstrate our results.     

Ultimate bound sets of a hyperchaotic system and its application in chaos synchronization

In this article, we investigate globally exponentially attractive sets and chaos synchronization for a hyperchaotic system, namely, Lorenz–Stenflo system. For this system, two ellipsoidal globally exponentially attractive sets are derived based on generalized Lyapunov function theory and the extremum principle of function. Furthermore, we propose linear feedback control with a one, two, three, and four inputs to realize globally exponential synchronization of two four‐dimesional hyperchaotic systems using inequality techniques. Numerical simulations are presented to show the effectiveness of the proposed synchronization scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 30–44, 2015     

Global exponential stability in Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions via LMI approach

In this paper, we study the global exponential stability in a Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions. Based on assuming that the activation functions are neither bounded nor monotonous or differentiable, several algebraic criterions in linear matrix inequality form for the global exponential stability in a Lagrange sense of the neural networks are obtained by virtue of Lyapunov functions and Halanay delay differential inequality. Meanwhile, the estimations of the globally exponentially attractive sets are given out. The results derived here are more general than that of the existing reference. Finally, two examples are given and analyzed to demonstrate our results.     

Global robust exponential stability analysis for stochastic interval neural networks with time-varying delays

In this paper, the global exponential stability is investigated for a class of stochastic interval neural networks with time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. Based on Lyapunov stable theory and stochastic analysis approaches, the delay-dependent criteria are derived to ensure the global, robust, exponential stability of the addressed system in the mean square. The criteria can be checked easily by the LMI control toolbox in Matlab. A numerical example is given to illustrate the effectiveness and improvement over some existing results.     

New estimations for ultimate boundary and synchronization control for a disk dynamo system

We consider globally exponentially attractive sets and synchronization control for a disk dynamo system. First, based on generalized Lyapunov function theory and the extremum principle of function, we derive some new 4D ellipsoid estimations and a polydisk domain estimation of the globally exponentially attractive set of a 4D disk dynamo system without existence assumptions. Our results improve existing results on the globally exponentially attractive set as special cases and can lead to a series of new estimations. Second, we propose linear feedback control with a single input or two inputs to realize globally exponential synchronization of two 4D disk dynamo systems using inequality techniques. Some new sufficient algebraic criteria for the globally exponential synchronization of two 4D disk dynamo systems are obtained analytically. The controllers designed here have a simple structure and less conservation. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.     

Stability in Lagrange sense for Cohen–Grossberg neural networks with time-varying delays and finite distributed delays

In this paper, we study the global exponential stability in Lagrange sense for a class of Cohen–Grossberg neural networks with time-varying delays and finite distributed delays. Based on the Lyapunov stability theory, several global exponential attractive sets in which all trajectories converge are obtained. We analyze three different types of activation functions which include both bounded and unbounded activation functions. These results can also be applied to analyze monostable as well as multistable and more extensive neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. Finally, one example is given and analyzed to verify our results.     

Global dissipativity of a class of BAM neural networks with time-varying and unbound delays

In this paper, we study the global dissipativity of a class of BAM neural networks with both time-varying and unbound delays. Based on Lyapunov functions and inequality techniques, several algebraic criteria for the global dissipativity are obtained. And the linear matrix inequality (LMI) approach is exploited to establish sufficient easy-to-test conditions which are related to the derivative of delay for the global dissipativity. Meanwhile, the estimations of the positive invariant set, globally attractive set and globally exponential attractive set are given out. Finally, two examples are presented and analyzed to demonstrate our results.     

Improved results on robust exponential stability criteria for neutral-type delayed neural networks

In this paper, we investigate the problem of robust global exponential stability analysis for a class of neutral-type neural networks. The interval time-varying delays allow for both slow and fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. Improved global exponential stability condition is derived by employing new Lyapunov-Krasovskii functional and the integral inequality. The developed nominal and robust stability criteria is delay-dependent and characterized by linear-matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples.