Averaging of Boundary-Value Problems with Parameters for Multifrequency Impulsive Systems

By using the averaging method, we prove the solvability of boundary-value problems with parameters for nonlinear oscillating systems with pulse influence at fixed times. We also obtain estimates for the deviation of solutions of the averaged problem from solutions of the original problem.     

Error Estimates for the Averaging Method for Pulse Oscillation Systems

We prove new theorems on the justification of the averaging method on a segment and semiaxis in multifrequency oscillation systems with pulse action at fixed times.     

变分Lyapunov方法和脉冲时滞微分系统的稳定性

By using the variational Lyapunov method and Razumikhin technique, the stability criteria in terms of two measures for impulsive delay differential systems are established. The known results are generalized and improved. An example is worked out to illustrate the advantages of the theorems.     

集合关于脉冲微分系统的稳定性

利用分段连续的李雅普诺夫函数及比较原理,通过建立比较原理,把集合对脉冲微分系统稳定性的判定化成集合对脉冲微分方程稳定性的判定.     

An Averaging Method for Singularly Perturbed Systems of Semilinear Differential Inclusions with C 0-Semigroups

We consider a system of two semilinear differential inclusions with infinitesimal generators of C ₀-semigroups. The nonlinear terms are of high frequency with respect to time and periodic with a specified period. Moreover, they are condensing in the state variables (x,y) with respect to a suitable measure of noncompactness. The goal of the paper is to give sufficient conditions to guarantee, for ∈>0 sufficiently small, the existence of periodic solutions and to study their behaviour as ∈→0. The main tool to achieve this is the topological degree theory for uppersemicontinuous, condensing vector fields.     

遍历性及其应用──(Ⅱ)某些动力系统的平均方法(英文)

把遍历函数的一般理论应用于某些动力系统的平均方法中去,阐述了在解含有小参数和非线性微分方程应用平均方法的基本思想．主要结果是引理２．１及定理２．２,在引理２．１中证明：当函数是遍历时,可用平均方法给出一个几乎恒等变换ｘ＝ｙ＋εｕ把非自治系统化为自治系统,此变换是可逆的,从而变换后的方程保持原有方程的性质．在此基础上,在定理２．２中,建立了此类方程的广义概周期解的存在及唯一性,最后给出一个例子,指出如果没有遍历性的假设,平均方法不能有效使用的原因．     

Averaging of Systems with Slow Variables

We justify the averaging method for systems with delay described by both slow and fast variables. The results obtained are applied to the analysis of one problem in control theory.     

一类带有脉冲扰动时滞互惠系统的持久性

研究了一类带有时滞和脉冲的互惠Ayala-Gilpin系统,并且得到系统持久性的充分条件,结论改进和推广了已知的结果.     

T-S模糊系统的脉冲稳定性

针对模糊控制系统提出了一种新的稳定性设计方法.该方法在传统T-S模型的局部子系统中引入脉冲控制项,构造了具有脉冲影响的模糊控制系统.然后,通过去模糊化技术,把具有脉冲影响的模糊系统转化为脉冲微分系统.这样,借助脉冲微分方程的比较原理和线性矩阵不等式技术,给出了模糊系统的脉冲稳定的充分条件.从而建立了模糊系统的简单脉冲控制策略.     

脉冲系统输入—输出到状态稳定的Lyapunov条件

在一定的条件下,通过对时间域分割成不同的区间段然后应用Lyapunov函数分析方法给出了脉冲系统输入—输出到状态稳定(IOSS)的一个充分条件,另外,讨论了积分输入—输出到状态稳定的情况.     

脉冲差分系统的Robust稳定性

运用Lyapunov函数法分析并建立了脉冲差分系统结构扰动下的R obust稳定性准则.     

常微分系统的脉冲镇定

本文考察了较一般形式的常微分系统的脉冲镇定问题,借助Lyapunov方法得到了该系统可脉冲指数镇定的充分判据,并给出了脉冲控制函数的具体算法．全文突出了脉冲在方程稳定性方面的控制效果,所得结果推广、改进了已有的相关结论．     

Averaging in Boundary-Value Problems for Systems of Differential and Integrodifferential Equations

Ukrainian Mathematical Journal - The averaging method is applied to the investigation of the problem of existence of solutions of boundary-value problems for systems of differential and...     

带脉冲的p-Laplacian系统的周期解研究

本文用变分法研究了一类带脉冲的p-Laplacian周期解的存在性问题.其中特别强调了脉冲效应,得到了由脉冲生成的解.特别地,非线性项可以取为零,当p=2时,我们的结果可以用来研究差分方程的周期解的存在性.     

Controllability Results for Second Order Neutral Impulsive Integrodifferential Systems

In this paper, we address the problem of controllability for abstract second order neutral integrodifferential systems with impulsive conditions in Banach spaces. Furthermore, we discuss the controllability of second-order neutral integrodifferential systems in finite dimensional spaces. The results are obtained by using strongly continuous cosine families of operators and the Banach fixed point theorem.