一类多平衡点线性切换系统稳定区域的估计

本文研究了多平衡点线性切换系统稳定区域的估计问题, 并得到了估计该类系统稳定区域的新结果. 利用分量最终界法, 不仅得到了多平衡点线性切换系统在任意切换路径下稳定区域的估计, 而且得到了多平衡点线性切换系统在停留时间不小于其最小停留时间的任意切换路径下稳定区域的估计. 与现有的结果相比, 新得到的稳定区域的估计更加精确, 在一定程度上减少了估计的保守性. 最后, 数值实例的结果验证了上述结果的正确性和有效性.     

多平衡点二维线性时不变切换系统的稳定性及镇定性

研究含不稳定子系统的多平衡点二维线性时不变切换系统的稳定性和镇定性问题.首先,在每一子系统仅有唯一焦点或中心、不同子系统的平衡点互异的情形下,确定含所有子系统平衡点的唯一特定区域,据此给出系统区域稳定的概念;然后,基于区域稳定的定义,利用解析法得到系统全局区域渐近稳定的简单判据,并设计了全局区域渐近镇定控制器及其算法.最后,通过数值仿真算例表明了所得结果的有效性和易操作性.     

联想记忆神经网络局部指数稳定的充要条件及特征函数

讨论非线性连续联想记忆神经网络平衡点局部指数稳定的判定条件及平衡点指数 吸引域的估计,得到了平衡点局部指数稳定的充要条件,并引入一个特征函数,可以判定平衡 点的邻域是否为指数吸引域.文中给出一族范数下(所有单调范数)网络局部或全局指数稳定 的判定条件,推广了已知文献在特定范数下所得到的结论.     

不确定双向联想记忆神经网络的稳定性分析

对双向联想记忆神经网络研究了平衡点的鲁棒稳定性.该网络的参数不确定,并且有时变时滞.当神经网络的激励函数满足Lipschitz连续性条件时,通过选取合适的Lyapunov-Krasovskii函数,建立了两个全局鲁棒稳定判据.由于这些判据考虑了神经元激励作用和抑制作用对网络的影响,他们和时变时滞的数值无关,并且易于使用内点算法进行检验.在注释中和已有的结果进行了对比.两个数值例子展示了所得结果的有效性.     

基于精确罚函数的一类广义非线性神经网络模型

针对一般的非线性优化问题定义了一种2次非线性罚函数,证明了在一定条件下对 应的罚优化问题的精确罚定理,由此引进了一种广义非线性神经网络模型,并证明了这种网络 的平衡点与能量函数之间的联系,在一定条件下对应的平衡点收敛到原问题的最优解.这种神 经网络模型对于求解许多优化问题具有重要的作用.     

离散多平衡点正切换系统有限区间稳定与镇定

在切换事件中,外界环境的干扰或者事物自身的发展变化会导致多平衡点现象.此时,多平衡点切换系统模型比传统的切换系统模型更适合描述此类事件.因此本文研究离散多平衡点正切换线性系统在有限时间区间上的稳定性与镇定性.第1,给出离散多平衡点线性切换系统为正的充要条件.第2,提出离散多平衡点正切换线性系统在有限时间区间上稳定的概念.第3,通过构造合适的Lyapunov函数以及合理分配系统的驻留时间与切换次数,针对部分子系统不稳定的离散多平衡点正切换线性系统,建立所考虑的自治系统有限时间稳定的充分条件.第4,给出非自治多平衡点正切换线性系统的控制器设计.最后,仿真例子验证理论结果的正确性.     

变时滞神经网络的全局指数稳定性

利用M矩阵理论,同构理论以及不等式技巧,研究了一类变时滞神经网络平衡点的存在性和惟一性问题。同时利用M矩阵理论,反证法以及不等式技巧,得到了变时滞神经网络系统惟一的平衡点的全局指数稳定性的充分条件。通过判断由神经网络的权系数、自反馈函数以及激励函数构造的矩阵是否为M矩阵,即可以检验该变时滞神经网络系统的全局指数稳定性。该判据易于用Matlab进行检验,最后给出一个仿真示例进一步证明了判据的有效性。     

基于分岔理论的永磁同步电机有限时间混沌控制

永磁同步电机运行系统具有不稳定的分岔特性,随着系统参数的变化,系统会在平衡点处发生分岔行为.首先,基于分岔理论构建了永磁同步电机的混沌模型.其次,通过研究系统的分岔参数,分析了系统在平衡点处的分岔特性,发现系统在零平衡点处会产生静态分岔并出现新的平衡点,随着参数的继续变化,系统在新的平衡点处发生连续的Hopf分岔,而连...     

一类变时滞神经网络的全局指数稳定性

在不要求激活函数有界的前提下,利用Lyapunov泛函方法和线性矩阵不等式(LMI)分析技巧,研究了一类变时滞神经网络平衡点的存在性和全局指数稳定性.给出判别网络全局指数稳定性的判据,推广了现有文献中的一些结果.这些判据具有LMI的形式,进而易于验证.仿真例子表明了所得结果的有效性.     

一类缺乏明确平衡点的不确定系统的部分变量镇定

针对一类缺乏明确平衡点的不确定系统,研究了系统部分变量的稳定性问题. 提出了将一致最终有界和渐近稳定相结合的系统稳定性模式,并给出了该系统稳定性模式的条件. 基于该稳定性模式,提出了阻尼配置控制方案,使系统部分变量在不同阶段稳定于给定运行区域和原点. 所开展的研究工作拓展了不确定系统的稳定性研究,解决了工业应用中普遍存在的一类缺乏明确平衡点的不确定系统的部分变量控制问题. 永磁同步电机的仿真验证了研究结果的有效性和实用性.     

Stability of nonlinear systems: A structural approach

This paper presents sufficient conditions for absolute stability of the equilibrium (null solution) of feedback systems containing a single nonlinearity satisfying the positive infinite sector condition. Most of the existent sufficient conditions for this problem are based on frequency domain analysis. The conditions presented here are based on the realizability of the feed-back system in a ‘Jacobi sign stable’ structure constituting thereby an alternative algebraic criterion for absolute stability. A more general result is also derived, for the case of many nonlinearities, by using some previous results on ‘Qualitative Stability’ and a theorem by S. K. Persidskii. Examples are presented showing the advantages of a structural approach in stability analysis.     

Stability analysis in a second-order differential equation with delays

A second-order differential equation with finite discrete delays is considered. Local stability of the zero equilibrium is investigated, and we obtain some sufficient conditions for the zero equilibrium is stable or unstable. Moreover, it is found that there exist the local Hopf bifurcations of the system when the delay varies.     

动态神经网络的输入2状态稳定性分析

针对非自治的动态神经网络系统，建立了动态神经网络的数学模型．并将其等效成一个非线性仿射控制系统．深入分析了该系统平衡点的存在性、唯一性和全局渐近稳定性，给出了系统输入-状态稳定的充分条件，构建了ISS-Lyapunov函数，并应用该函数确保了系统的全局渐近稳定性．     

On a method for studying stability of nonlinear dynamic systems

A method for studying the stability of the equilibrium points of linearized, nonlinear dynamic systems of arbitrary order is considered. The method is based on the fact that, due to the nature of the mutual arrangement of the trajectories of the corresponding linearized system, and the boundaries of some simply-connected, bounded neighborhood of its equilibrium point, one can judge the asymptotic stability and instability of both this point and the equilibrium point of the nonlinear system. Necessary and sufficient conditions of asymptotic stability and sufficient conditions of instability of equilibrium points of linear systems are given. Together with the theorems of the first Lyapunov method, these conditions determine the sufficient conditions of asymptotic stability and instability of equilibrium points of nonlinear systems. In some cases, the proposed conditions may turn out to be preferable to the known ones.     

柔性手抓持平面物体的最佳状态分析

本文将柔性手抓持物体的细微平面运动力学模型简化成质量刚度系统,导出物体系统的广义平移刚度、广义扭转刚度、广义耦合刚度.引进抗扰动指标作为衡量系统承受扰动力和力矩的综合效应.分析了系统平衡状态的稳定性条件,并认为在满足静力平衡条件、状态选择条件和稳定性条件下.抗扰动指标取得最大值时为最佳抓持状态.采用非线性规划理论进行系统综合.最后以A3-A3-A3型柔性手抓持椭圆为例,进行数值求解.     

一类多时间尺度机电耦合系统降阶及稳定一致性

针对一类机电耦合系统,讨论了非线性多时间尺度系统与其相应的简化降阶系统稳定性一致问题,给出了稳定一致性的条件;讨论了多时间尺度系统(原始系统)和降阶系统的稳定域边界问题,分析了非线性多时间尺度系统稳定域边界对摄动参数ε的连续依赖性,给出了稳定边界对ε连续依赖的条件.研究表明不论对系统的平衡点稳定性还是稳定域来说,在可接受的条件下略去快动态是合理的.     

非线性微分代数系统的稳定性

本文发展了微分代数系统的稳定性理论,讨论了微分代数系统在平衡点近旁的正则性问题、给出了在平衡点处的受限形式,建立了受限系统Ｌｙａｐｕｎｏｖ稳定性的基本定理,得到了微分代数系统平凡解渐近稳定的判别准则。     

Non-existence of finite-time stable equilibria in fractional-order nonlinear systems

We note that in the literature it is often taken for granted that for fractional-order system without delays, whenever the system trajectory reaches the equilibrium, it will stay there. In fact, this is the well-known phenomenon of finite-time stability. However, in this paper, we will prove that for fractional-order nonlinear system described by Caputo’s or Riemann–Liouville’s definition, any equilibrium cannot be finite-time stable as long as the continuous solution corresponding to the initial value problem globally exists. In addition, some examples of stability analysis are revisited and linear Lyapunov function is used to prove the asymptotic stability of positive fractional-order nonlinear systems.     

New criteria for globally exponential stability of delayed Cohen–Grossberg neural network

This paper is concerned with analysis problem for the global exponential stability of the Cohen–Grossberg neural networks with discrete delays and with distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, we employ Lyapunov functions to establish some sufficient conditions ensuring global exponential stability of equilibria for the Cohen–Grossberg neural networks with discrete delays and with distributed delays. Our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed neural networks.     

Global stability of bidirectional associative memory neural networks with continuously distributed delays

Global asymptotic stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with continuously distributed delays is studied. Under two mild assumptions on the activation functions, two sufficient conditions ensuring global stability of such networks are derived by utilizing Lyapunov functional and some inequality analysis technique. The results here extend some previous results. A numerical example is given showing the validity of our method.