线性时滞系统的时滞相关稳定性分析

对于存在状态时滞的线性时滞系统,分为固定时滞及时变时滞两种情形,基于Lyapunov-Krasovskii理论分析稳定性,通过时滞划分,得到以LMI形式给出的一种保守性小的渐近稳定性条件,且能够处理任意变化的变时滞问题.实例表明只需粗略划分就能大大提高保守性能,为了兼顾计算负担,r取较小数值即可.并且LMI中的决策变量少,形式简洁.     

一类带有竞争和自反时滞的网站竞争系统的Hopf分支

不同于以往研究网站竞争系统时,仅考虑带有自反时滞或竞争时滞的情况,本文研究了一类同时带有竞争时滞和自反时滞的网站竞争系统,并以时滞作为分支参数,通过分析正平衡点处的特征方程,研究了正平衡点的稳定性,证明了Hopf分支的存在性,得到了发生Hopf分支时的临界的时滞值,最后通过数值模拟进一步验证了所得结论.     

非线性随机时滞系统的时滞反馈鲁棒H∞控制

本文研究了具有变时滞的非线性随机时滞系统的时滞反馈鲁棒H∞控制问题.利用时滞分割技术,构造了新的Lyapunov-Krasovskii泛函,通过Ito公式,以线性矩阵不等式(LMI)的形式给出了时滞反馈鲁棒H∞控制器存在的充分条件,通过数值仿真算例说明了结论的正确性和方法的有效性.     

变时滞的退化滞后型微分系统的稳定性

主要研究了具有变时滞的退化时滞微分系统的稳定性.利用退化时滞微分系统的变易公式和Gronwall-Bellman积分不等式给出了该系统的指数估计以及稳定和指数渐近稳定的充分条件.     

一类具有状态及控制滞后的不确定系统的时滞相关鲁棒H∞控制

讨论了一类同时具有状态时滞与输入时滞的不确定系统的时滞相关鲁棒H∞控制问题．借助于积分不等式，用线性矩阵不等式方法获得了系统时滞相关与时滞导数相关的鲁棒H∞控制器的设计方法．不需要对原系统进行模型变换．     

若干类时滞切换系统的稳定性问题

主要研究了镇定切换系统的鲁棒稳定性问题.用切换lyapunov函数方法,通过定义指标函数,讨论了基于切换lyapunov函数的若干类时滞切换系统的稳定性问题,用矩阵不等式研究了时滞,时滞摄动和不确定时滞的切换系统的鲁棒稳定性.     

不确定时滞Lurie系统的鲁棒绝对稳定性分析

研究了一类不确定Lurie时滞系统的鲁棒绝对稳定性问题，不确定项范数有界。通过构造特殊的李亚普诺夫函数，分别考虑了时滞相关和时滞无关两情况，得到了系统鲁棒绝对稳定的充分条件。     

具有时滞和非时滞耦合的复杂动态网络的自适应同步

对于同时具有时滞耦合和非时滞耦合的复杂动态网络,以时滞动力系统的稳定性理论为基础,设计了全新的自适应控制器,同时给出了一些简单而又一般的网络同步化准则.对由三个节点组成的动态网络的同步化进行了数值模拟,使得理论分析与数值模拟得到了相互验证.     

具时变时滞和无穷时滞及反馈控制的n-种群竞争模型的周期解

研究更为广泛的同时具有交时滞,无穷时滞及反馈控制的n-种群竞争模型,并且以重合度理论和Lyapunov泛函为主要工具,得到了保证模型正周期解存在和全局吸引的充分性条件,所得结论推广了已有结果.     

一类简化的时滞半导体激光方程的Hopf分岔

研究一类简化的时滞半导体激光方程的稳定性和Hopf分岔.以时滞量为参数,分析系统线性化方程零解的稳定性,给出系统产生Hopf分岔临界时滞表达式,最后用数值模拟对结论进行验证.     

Cucker–Smale flocking under rooted leadership and time-varying heterogeneous delays

In this paper, a Cucker–Smale model with time-varying heterogeneous delays in the communication process is investigated, where the delay on each communication link is time-varying and independent of other communication links. A general update rule based on the distance between agents is used to determine the edge weights of the communication network. The method of constructing augmented system is used so that the system stability is transformed into a product convergence problem of time-varying sub-stochastic matrices equivalently. By analyzing this convergence problem, a sufficient condition is established to achieve flocking, which relates to the initial states, the structure of communication network and the upper bound of time delays.     

Stability of Hopfield-type neural networks II

The global asympatotic stability and asymptotic stability for Hopfield-type neural networks with delays are investigated. Project supported by the National Natural Science Foundation of China.     

分布时滞系统的动态输出反馈鲁棒稳定

主要研究了一类具分布时变时滞不确定系统的输出反馈鲁棒稳定问题.基于动态输出反馈和Lyapunov-Krasovskii泛函,给出了闭环系统与时滞相关的鲁棒稳定的条件.所得条件为线性矩阵不等式形式,便于运用内点算法进行求解.     

SOME NEW RESULTS ON THE PERMANENCE OF A LOGISTIC TYPE SYSTEM WITH TIME DELAYS

In this paper, we study a class of Logistic type system with both discrete delays and continuous delays. Some new criteria on the permanence of the system are established. An example shows the feasibility of our main results.     

关于变时滞Lur’e间接控制系统的绝对稳定性

本文研究了变时滞Lur’e间接控制系统的绝对稳定性.利用M-矩阵性质及不等式技巧,通过引进可调参数,得到了变时滞Lur’e间接控制系统与时滞相关绝对稳定性新的充分条件.文中的结论推广和改进了已有文献中相应结果.     

一类偏泛函微分方程的Hopf分支

讨论了一类具有限时滞含迁移的Prey-Predator系统平衡态的稳定性和Hopf分支,表明当系统的6个独立参数在一定范围内取值时,随着时滞的增加,系统平衡态的稳定性在一定范围内交替变化,而每一次平衡态稳定性的改变都相伴有Hopf分支发生.     

Dissipativity of Runge-Kutta methods for dynamical systems with delays

This paper is concerned with the numerical solution of dissipativeinitial value problems with delays by Runge-Kutta methods. Asufficient condition for the dissipativity of the systems isgiven. The concepts of D(l)-dissipativity and GD(l)-dissipativityare introduced. We investigate the dissipativity propertiesof (k,l)-algebraically stable Runge-Kutta methods with piecewiseconstant or linear interpolation procedures for finite-dimensionaland infinite-dimensional dynamical systems with delays.     

时滞方程解的振动性和正解的存在性

本文建立了具有分布时滞的一阶线性微分方程解的振动准则和正解存在的充分条件．     

Profitless delays for extinction in nonautonomous Lotka-Volterra system

IntroductionCOnsider the folbeing 8ystem of differentiaJ equations'This system models competition among n species. Here xi(t) denotes the concentration of theith specthe at thoe t, and bi(t) is it5 growth rate at this time, a,j(t) denote the competitivecoefficient between the ith species and the jth species, and when i = j, aij(t) denotes thedensity-dependent rate of the ith species; n(t) is the time deviating argUments at time t(i,j = l,2,',n). As n(t) - 0 for j = l,',n, system (1) is k…     

Exponential stability criteria of uncertain systems with multiple time delays

The exponential stability (with convergence rate α) of uncertain linear systems with multiple time delays is studied in this paper. Using the characteristic function of linear time-delay system, stability criteria are derived to guarantee α-stability. Sufficient conditions are also obtained for exponential stability of uncertain parametric systems with multiple time delays. For two-dimensional time-invariant system with multiple time delays, the proposed stability criteria are shown to be less conservative than those in the literature. Numerical examples are given to illustrate the validity of our new stability criteria.