时标动力学方程的稳定性

本文主要研究非自治时标动力学方程x△=f(t,x),(t,x)∈T×Rn的平凡解稳定、一致稳定、渐近稳定,与不稳定的充分必要条件.在定理的证明中充分性主要利用K类函数严格单调递增和Lyapunov函数的连续性;必要性的证明中,分别构造Lyapunov函数,满足定理的条件,使得定理的结论成立.     

Dynamics for Controlled 2D Generalized MHD Systems with Distributed Controls

We study the dynamics of a piecewise (in time) distributed optimal control problem for Generalized MHD equations which model velocity tracking coupled to magnetic field over time. The long-time behavior of solutions for an optimal distributed control problem associated with the Generalized MHD equations is studied. First, a quasi-optimal solution for the Generalized MHD equations is constructed; this quasi-optimal solution possesses the decay (in time) properties. Then, some preliminary estimates for the long-time behavior of all solutions of Generalized MHD equations are derived. Next, the existence of a solution of optimal control problemis proved also optimality system is derived. Finally, the long-time decay properties for the optimal solutions is established.     

一般时间尺度上时滞脉冲系统的双测度稳定性

讨论了一般时间尺度上时滞脉冲系统的双测度稳定性问题.我们引进了一个新的概念即一般时间尺度上时滞脉冲系统的(h_0,h)稳定性.利用Lyapunov函数法和分析法得到了一般时间尺度上时滞脉冲系统解的双测度稳定性判据.最后给出了一个例子以说明本文结论的有效性.     

Global Stability of a Stochastic Lotka-Volterra Cooperative System with Two Feedback Controls

In this paper, a class of Lotka-Volterra cooperation system and corresponding stochastic system with two feedback controls which are a?ected by all species are considered. We obtain some su?cient criteria for local stability and global asymptotic stability of equilibria of the systems. Our study shows that these equilibria could be globally stable by adjusting coe?cients of the feedback control variables and stochastic perturbation parameters. Numerical simulations are presented to demonstrate our main result.     

时变离散大系统的稳定性

本文首先给出了线性时变离散系统稳定性的一个充分条件.然后研究当孤立子系统满足上述条件时的线性及非线性时变离散大系统的稳定性.利用向量李雅普诺夫函数法结合时变离散系统的比较原理,得到了时变离散大系统在稳定性中的集结模型.直接由集结系统的稳定性得到大系统稳定性的条件.     

Stability of Linear Integrodifferential Systems with Time-varied Confficients with Large Scale

51.IntroductionConsideralinearintegrodifferentialsystemswithtime-variedconfficientswherex6R",A(t)isanXnrealmatrixfunctioncontinuousforoO.ManyscholarshavecontributedtheirpaPers[1-4]todiscussstabilityofzerosolutionofsystem(1.l).Inthispaper,weassumethatsystem(1.1)canbedecomPOsedintotheform=n,A,j(t)isaniXnjrealmatrixfunctioncontinuousforo相似文献   

Exponential Stability of Singularly Perturbed Systems with Time Delay

In this article, we study the exponential stability of singularly perturbed systems with time delay. By using vector delay inequalities and Lyapunov functions, exponential stability criteria are derived for both linear and some classes of nonlinear singularly perturbed systems with time delay. Examples are given to verify the stability criteria.     

两类时滞系统的鲁棒性分析

考虑了两类具有参数不确定性的时滞系统的鲁棒稳定性问题, 给出了系统具有鲁棒性能的几个充要条件. 这些结论对于研究具有时滞的反馈控制系统有重要的理论和实践价值.     

解大系统稳定性的积分方程法

本文通过分解积分方程组，并建立积分方程法比较原理，化大系统为低维系统，进而讨论了带时滞的时变大系统的稳定性，给出了新的结果，这一方法也可以用来讨论其它类型大系统的稳定性问题．     

时滞随机耦合网络的稳定性

利用Lyapunov方法和图论研究一类时滞随机耦合网络的稳定性,给出一种构造Lyapunov泛函的方法,建立一系列与网络的拓扑结构相关的稳定性判据.     

初始时刻不同的奇异系统的稳定性

给出了初始时刻不同的奇异系统实用稳定性的定义,利用比较原理和Lyapunov函数方法研究了初始时刻不同的奇异系统的实用稳定问题,并得到了系统实用稳定性的判定准则.     

一类单滞量Kolmogorov型捕食-食饵系统的稳定性分析

本文给出了一类单滞量Kolmogorov型捕食-食饵系统的正平衡态线性渐近稳定的充要条件,这些条件易于检验和应用．     

线性离散大系统的稳定性

本文直接运用线性范数型Liapunov函数处理线性定常和时变离散大系统的稳定性,得到了渐近稳定若干判别准则.     

The Stability of Systems of Neutral Type with Small Time Lag

In this paper, we have obtained the equivalence theorems of stability between the system of differential equations $[{\dot x_i}(t) = \sum\limits_{j = 1}^n {{a_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{b_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{c_{ij}}{{\dot x}_j}(t)} (i = 1,2, \cdots ,n)\]$ and the system of differential-difference equations of neutral type $[{\dot x_i}(t) = \sum\limits_{j = 1}^n {{a_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{b_{ij}}{x_j}(t - {\Delta _{ij}})} + \sum\limits_{j = 1}^n {{c_{ij}}{{\dot x}_j}(t - {\Delta _{ij}})} (i = 1,2, \cdots ,n)\]$ where a_ij, b_ij, c_ij are given constants, and \Delta_ij are non-negative real constants.     

时滞切换神经网络系统的鲁棒指数稳定性

研究了具有时间滞后切换不确定细胞神经网络(UCNNs)系统的指数稳定性.利用同胚映射和M矩阵理论,得到UCNNs系统平衡点存在性,唯一性和指数稳定性的充分条件;利用平均驻留时间方法,研究了时滞切换UCNNs系统限制切换下的鲁棒指数稳定性,并得到确保系统全局指数稳定的充分条件.     

一类时滞连续模糊系统稳定性研究

对一类状态时滞连续模糊系统模型稳定性进行了研究,基于Lyapunov稳定性理论证明其系统的稳定性,利用线性矩阵不等式(LMI)方法,得到其稳定的一个充分条件.最后用数值例子进一步说明本文所给方法的有效性.     

线性时变切换系统的渐近稳定性研究

考虑一类线性时变切换系统的渐近稳定性.基于矩阵测试理论,文中给出线性时变切换系统在周期切换和等时切换下渐近稳定的充分条件,并通过仿真实例说明结论是正确的.     

时滞影响下受控斜拉索的参数振动稳定性

研究了轴向激励作用下受控斜拉索系统主参数共振的时滞效应,考虑了拉索垂度和几何非线性的影响,基于Hamilton变分原理建立了受控斜拉索系统轴向激励下的非线性参数振动方程,利用Galerkin方法得到时滞动力系统,运用多尺度法对受控系统的主参数共振进行了分析,得到了不同时滞值、控制增益时参数振动稳定域和受控拉索的时程曲线.研究表明,时滞影响下斜拉索振动控制系统的效果变差,参数共振的稳定域发生偏移,对受控斜拉索系统的控制效果随着时滞的增大而变差,从而对控制系统的参数设计起到指导作用.     

Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays

In this paper, the problem of robust exponential stability is investigated for a class of stochastically nonlinear jump systems with mixed time delays. By applying the Lyapunov–Krasovskii functional and stochastic analysis theory as well as matrix inequality technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. Time delays proposed in this paper comprise both time-varying and distributed delays. Moreover, the derivatives of time-varying delays are not necessarily less than 1. The results obtained in this paper extend and improve those given in the literature. Finally, two numerical examples and their simulations are provided to show the effectiveness of the obtained results.