具有时滞的复杂动态网络的无源性

研究了复杂时滞动态网络的无源性.通过构造适当的Lyapunov泛函,得出了两个使得复杂网络无源的充分条件.最后,通过一个具体的例子及其仿真来阐明得到的条件的有效性.     

网络化马尔可夫跳变系统的鲁棒无源控制

针对基于网络的凸多面体不确定离散时间马尔可夫跳变系统,研究其鲁棒无源控制问题.在网络诱导时滞是时变且有界的情况下,基于李雅普诺夫稳定性理论,通过构造参数依赖的随机李雅普诺夫泛函和运用广义系统变换,提出了不依赖模态的无源控制器存在的时滞依赖充分条件.所设计的鲁棒无源控制器保证了相应的闭环系统是鲁棒随机稳定且具有指定耗散率.将鲁棒无源控制器设计问题转化为一组线性矩阵不等式的可解性问题.仿真算例证明了本文方法的有效性.     

基于观测器的非线性不确定时滞跳变系统无源控制

该文基于鲁棒控制理论,采用线性矩阵不等式(LMI)方法,研究了一类非线性不确定时滞Markov跳变系统的无源控制问题,设计了基于观测器的无源控制器.通过构造合适的Lyapunov函数,给出了对所有允许的不确定、时滞和非线性,被控对象满足无源控制指标约束下系统渐近稳定的一个充分条件.求解一个线性矩阵不等式,即可获得系统的无源控制器.仿真示例显示了该文设计方法的有效性.     

具有不确定性的分数阶时滞复值神经网络无源性

该文研究了一类具有不确定性和时滞的分数阶复值神经网络无源性问题,未将复值神经网络模型拆分成两个实值系统,而是将复值系统当成一个整体直接进行处理.通过构造恰当的Lyapunov函数,并利用矩阵不等式技巧,建立了网络无源性的线性矩阵不等式判据.给出的数值例子和仿真验证了获得结论的可行性和有效性.     

一类基于广义无源性的随机切换时滞系统的异步输出调节问题

文章讨论一类具有时变时滞的随机切换系统基于广义无源性的异步输出调节问题.采用改进的自由权矩阵方法并且选择新的随机Lyapunov-Krasovskii泛函来降低保守性.设计时滞全息反馈控制器和时滞误差反馈控制器,结合外部系统来消除外部扰动的影响.采用伊藤公式来处理随机问题.结合平均驻留时间方法、自由权矩阵技术、Jensen积分不等式,在异步切换下得到基于广义无源性的输出调节问题可解的充分条件.最后,用两个数值例子验证所给方法的有效性.     

Markov切换时滞基因调控网络的均方同步和随机无源同步北大核心CSCD

基因调控网络(GRNs)及其动力学模型的研究在后基因组时代是一个重要的研究领域.定性分析基因调控网络及其动力学对系统地认识生物体具有重要意义.该文提出了一类具有时变时滞和Markov切换的随机基因调控网络模型,研究了其均方同步和随机无源同步问题.通过设计合适的Lyapunov-Krasovskii泛函(LKF),并利用Lyapunov稳定性理论、线性矩阵不等式方法和随机分析技巧,得到了均方同步和随机无源同步的充分条件.此外,通过与其他文献进行比较,显示了该文结果的理论价值.数值模拟验证了所得充分条件的有效性.     

具时滞和记忆项的非线性粘弹性波动方程解的爆破——纪念阳名珠先生

本文研究一类具时滞和记忆项的非线性粘弹性波动方程的初边值问题.对初始条件、时滞项、记忆项、非线性源项和阻尼项附加适当的条件,利用凸性方法证明了能量解的爆破性,从而推广了已有文献的结果.     

具有营养循环和时滞的浮游生物系统的稳定性及Hopf分支

建立并研究了具有营养循环和时滞的浮游动植物模型,模型中描述浮游动植物间的相互作用函数是Holling-Ⅲ型功能反应函数.首先讨论了模型解的正性及有界性,然后分析了系统在无时滞和有时滞两种情况下边界平衡点和正平衡点的局部稳定性,并通过建立适当的Lyapunov函数,讨论了平衡点的全局稳定性.研究表明,随着时滞的增加,系统会出现Hopf分支.     

内部输入带不同时滞的Timoshenko梁的指数稳定性

研究了内部输入带不同时滞的Timoshenko梁的指数稳定性.利用Smith预估器的思想,对部分状态进行预估可得无时滞系统.对无时滞系统设计控制器,得到闭环系统.通过讨论闭环系统的稳定性及原时滞系统和无时滞系统的误差系统的指数衰减,最终得出原系统的指数稳定性.     

时滞对食物受限种群演化模型的渐近性的影响

该文主要是研究时滞对食物受限的种群演化模型的渐近形态的影响.通过与非时滞系统相比较,得到 了时滞对解的渐近性的影响估计.     

Passivity analysis of neural networks with Markovian jumping parameters and interval time-varying delays

In this paper, the problem of passivity analysis is investigated for neural networks with Markovian jumping parameters, interval time-varying delays and norm bounded parameter uncertainties. The delay-dependent passivity conditions are derived for two types of interval time-varying delay in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are given to show the effectiveness of the proposed conditions.     

New results on exponential passivity of neural networks with time-varying delays

The problem of delay-dependent exponential passivity analysis is investigated for neural networks with time-varying delays. By use of a linear matrix inequality (LMI) approach, a new exponential passivity criterion is proposed via the full use of the information of neuron activation functions and the involved time-varying delays. The obtained results have less conservativeness and less number of decision variables than the existing ones. A numerical example is given to demonstrate the effectiveness and the reduced conservatism of the derived results.     

Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term

In this paper, the problem of passivity analysis is investigated for neutral type neural networks with Markovian jumping parameters and time delay in the leakage term. The delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing proper Lyapunov–Krasovskii functional, new delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). Moreover, it is well known that the passivity behavior of neural networks is very sensitive to the time delay in the leakage term. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed method.     

Passivity analysis of Markovian switching complex dynamic networks with multiple time-varying delays and stochastic perturbations

This paper is concerned with the passivity problem for a class of Markovian switching complex dynamic networks with multiple time-varying delays and stochastic perturbations. Some sufficient conditions are obtained to guarantee that the complex dynamic networks with multiple time-varying delays and stochastic perturbations under Markovian switching are passive in the sense of expectation. The appropriate stochastic Lyapunov–Krasovskii functional was constructed, and stochastic theory, linear matrix inequality technique and properties of Weiner process were employed to achieve the results. Finally, some simulation examples are presented to illustrate the effectiveness of the obtained results.     

具变时滞的非线性退化微分系统的渐近稳定性判据

In this paper, the asymptotic stability for singular differential nonlinear systems with multiple time-varying delays is considered. The V-functional method for general singular differential delay system is investigated. The asymptotic stability criteria for singular differential nonlinear systems with multiple time-varying delays are derived based on V-functional method and some analytical techniques, which are described as matrix equations or matrix inequalities. The results obtained are computationally flexible and efficient.     

Passivity analysis of Markov jump neural networks with mixed time-delays and piecewise-constant transition rates

In this paper, passivity analysis is considered for Markov jump neural networks with both mixed time-delays and time-varying transition rates. The mixed time-delays consist of both discrete and distributed delays. The time-varying character of transition rates is assumed to be piecewise-constant. By use of the linear matrix inequality (LMI) method and a Lyapunov functional that accounts for the mixed time-delays, a delay-dependent passivity condition is derived, which can be easily checked. The result presented depends upon not only discrete delay but also distributed delay. A numerical example is proposed to show the effectiveness of the proposed method.     

A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays

In this paper, the problem of exponential passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing new augmented Lyapunov-Krasovskii’s functionals and some novel analysis techniques, improved delay-dependent criteria for checking the exponential passivity of the neural networks are established. The proposed criteria are represented in terms of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. A numerical example is included to show the superiority of our results.     

Dissipative sampled‐data control of uncertain nonlinear systems with time‐varying delays

This article investigates the delay‐dependent robust dissipative sampled‐data control problem for a class of uncertain nonlinear systems with both differentiable and non‐differentiable time‐varying delays. The main purpose of this article is to design a retarded robust control law such that the resulting closed‐loop system is strictly (Q, S, R)‐dissipative. By introducing a suitable Lyapunov–Krasovskii functional and using free weighting matrix approach, some sufficient conditions for the solvability of the addressed problem are derived in terms of linear matrix inequalities. From the obtained dissipative result, we deduce four cases namely, H_∞ performance, passivity performance, mixed H_∞, and passivity performance and sector bounded performance of the considered system. From the obtained result, it is concluded that based on the passivity performance it is possible to obtain the controller with less control effort, and also the minimum H_∞ performance and the maximum allowable delay for achieving stabilization conditions can be obtained via the mixed H_∞ and passivity control law. Finally, simulation studies based on aircraft control system are performed to verify the effectiveness of the proposed strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 142–154, 2016     

Global Robust Passivity Analysis for Stochastic Interval Neural Networks with Interval Time-Varying Delays and Markovian Jumping Parameters

In this paper, the problem of passivity analysis is investigated for stochastic interval neural networks with interval time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov-Krasovskii functional, utilizing the free-weighting matrix method and some stochastic analysis techniques, we deduce new delay-dependent sufficient conditions, that ensure the passivity of the proposed model. These sufficient conditions are computationally efficient and they can be solved numerically by linear matrix inequality (LMI) Toolbox in Matlab. Finally, numerical examples are given to verify the effectiveness and the applicability of the proposed results.     

Robust synchronization of impulsively-coupled complex switched networks with parametric uncertainties and time-varying delays

This paper presents a general impulsively-coupled complex switched network (ICCSN) model with parametric uncertainties and multiple Time-varying Delays in both the linear and nonlinear terms. The model is more general than those in the literature in that it contains switching behaviors on nodes and impulsive effects in the whole topology. Robust synchronization of ICCSNs with parametric uncertainties and time-varying delays is investigated. Based on the Lyapunov stability theory, delay-independent synchronization conditions for ICCSNs with uncertainties and delays are obtained. In addition, we consider five special synchronization cases: ICCSNs with delays in both the linear and nonlinear terms, ICCSNs with parametric uncertainties and delays either in the linear or in the nonlinear term, ICCSNs without switching behaviors but with parametric uncertainties and delays, and impulsively-switched-coupled complex switched network with uncertainties and delays. A systematic-design procedure is presented, and a numerical example is carried out to demonstrate the effectiveness of the proposed synchronization strategy. A comparative study of the maximum impulsive intervals for synchronization is presented for all special cases.