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1.
关于变系数线性方程的稳定性   总被引:10,自引:0,他引:10  
本文给出了变系数线性方程有关稳定性的一些简洁的判据.对周期系数线性方程,给出了较为精确的渐近稳定性判据.从理论上解释了原先“冻结系数法”一般不能成立的原因.  相似文献   

2.
利用Lyapunov的方法讨论了时滞微分方程x.(t)=f(t,x(t),x(t-τ(t)))的全局指数渐近稳定性和全局渐近稳定性.  相似文献   

3.
在本文中,作者建立了一些定理可以确保系统:x(n 1)=f(n,xn)(1)为一致稳定、渐近稳定或一致渐近稳定。在所获得的定理中,不要求△V为常负,这里△V(n,xn)≡V(n 1,x(n 1)-V(n,x(n))=V(n 1,f(n,xn)))-V(n,x(n)),特别地,在定理1中,△V甚至可以恒为正,这大大地改进了已有结果并且更加便于应用。  相似文献   

4.
1 IntroductionConsider the functional differential equations (FDE's) with finite delay ofthe form:where x,(0) = x(t 0) for --r 5 0 5 0 with some r 2 0 and f: [T, co] x C RI with C = C([--r, 0], R') the space of continuous functions mapping [--r, 0]into l-dimensional real space RI. For any yi E C we define the norm of yi as:where l' I is any norm in RI.Inspired by the ideas in [l--3], we develop a new technique in this work tostudy the stability of FDE's, where the components xl) xZt…  相似文献   

5.
We study the asymptotic behavior of the solutions of a class of linear dissipative integral differential equations. We show in the abstract setting a necessary and sufficient condition to get an exponential decay of the solution. In the case of the lack of exponential decay, we find the polynomial rate of decay of the solution. Some examples are given.  相似文献   

6.
Stability of functional differential equations with impulses   总被引:1,自引:0,他引:1  
In this paper, the stability of functional differential equations (FDE) with impulses is investigated. Some comparison theorems are given. Several Lyapunov-Razumikhin functions of partial components of the state variable x, which can be much easier constructed, are used so that the conditions ensuring that stability are simpler and less restrictive. The results improve and generalize the ones in the literature. An example is also given to illustrate the importance of our results.  相似文献   

7.
本文研究的是随机脉冲微分方程的渐近p稳定性.首先给出一些预备知识,然后运用Lyapunov函数建立随机脉冲微分方程平凡解的渐近p稳定性的充分条件.  相似文献   

8.
This paper deals with the impulsive control for a class of differential systems with delay. Using Lyapunov functions and the comparison principle, we present some sufficient conditions for the asymptotic stability and exponential stability of impulsive control systems with delay. Moreover, we give an estimate of the upper bound of impulse interval. The results in this paper extend and improve the earlier publications. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

9.
一类广义模糊双向联想记忆的稳定性   总被引:2,自引:0,他引:2  
本文在(3)的基础上引入了一类广义的动态网络模型-带阈值的模糊双向联想记忆,并系统地研究了该网络的稳定性,证明了这个系统对于任意的连接权矩阵和阈值向量是全局稳定的,而系统的平衡态又是Lyapunov稳定的,最后用实例验证了我们的结论。  相似文献   

10.
1 IntroductionStability is an important perfermance index of concrete systems such asmanagement systems, power systems, engineering systems and so on. Forthe stability V--functional criterion method of functional differential systems,have had many results in recent years, see) for example, [1] and [2]. Andfor degenerate systems, papers [41-[81 have carefully discussed and given someimportant results. But we note that (see [9]) many concrete systems, besidescontain delay, are degenerate. So, f…  相似文献   

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