两类时滞耦合复杂网络的同步问题研究

发布时间：2018-05-24 12:01

本文选题：复杂网络 + 同步　；参考：《太原科技大学》2017年硕士论文

【摘要】：复杂网络是由具有一定特征和功能的节点,通过节点之间的相互影响和关联所形成的集合体。近年来,复杂网络得到来自不同领域学者的广泛关注。复杂网络的同步,指的是随着时间的推移,其所有节点的状态与目标节点的状态达到一致。由于网络同步不仅可以解释许多自然现象,而且具有潜在的应用价值,因此同步已成为研究的热点。由于网络结构的日益复杂化,时滞对复杂网络的影响是不可避免的,从而影响着网络同步的实现。学者们对时滞耦合复杂网络的同步问题进行了较为深入的研究。本文在分析了大量国内外文献的基础上,利用时滞分解法,通过选取适当的LyapunovKrasovskii泛函,结合线性矩阵不等式技术,对两类时滞耦合复杂网络的同步问题进行研究。具体而言,本论文的主要内容如下:(1)研究了一般时滞耦合复杂网络的同步稳定问题。为分析方便,将同步稳定问题转化为同步误差的关于零解的稳定问题。采用时滞分割方法将时滞区间分成两个相等的子区间和可调的子区间,分别为每个子区间构造不同的Lyapunov-Krasovskii泛函,利用互凸组合技术得到具有弱保守性的稳定性判据。最后给出数值算例表明本文所得结论的有效性。(2)研究了中立型时滞耦合复杂系统的同步稳定性问题。首先将同步稳定问题转化为同步误差的关于零解的稳定性分析问题。然后将时滞区间分成两个子区间,充分考虑时变时滞的有用信息,为每一个子区间选取不同的Lyapunov-Krasovskii泛函,最后结合互凸组合不等式技术和自由权矩阵的方法,得到了具有较低保守性的时滞相关同步稳定性判据。通过数值算例验证了结果的弱保守性。(3)当网络依靠自身的耦合作用不能实现同步时,研究了中立型时滞耦合复杂网络的同步控制问题。对网络节点施加一个简单的线性反馈控制器,将同步控制问题转化为误差系统的稳定性分析问题,利用时滞分解方法获得了同步稳定准则。通过求解线性矩阵不等式,可以获得最小的控制器增益。数值仿真例子表明结论的正确性。
[Abstract]:Complex network is a collection of nodes with certain characteristics and functions, which is formed by the interaction and association between nodes. In recent years, complex networks have received extensive attention from scholars in different fields. The synchronization of complex networks means that the state of all nodes is consistent with that of the target nodes over time. Because network synchronization can not only explain many natural phenomena, but also has potential application value, synchronization has become a hot research topic. Due to the increasing complexity of network structure, the influence of time delay on complex network is inevitable, thus affecting the realization of network synchronization. The synchronization problem of time-delay coupled complex networks has been studied deeply by scholars. Based on the analysis of a large number of literatures at home and abroad, the synchronization problem of two classes of time-delay coupled complex networks is studied by selecting appropriate LyapunovKrasovskii functional and combining with the technique of linear matrix inequality (LMI) by using the time-delay decomposition method. Specifically, the main contents of this thesis are as follows: 1) the synchronization stability problem of a general time-delay coupled complex network is studied. For the convenience of analysis, the problem of synchronization stability is transformed into the stability problem of zero solution of synchronization error. The delay-division method is used to divide the delay-interval into two equal subintervals and adjustable subintervals, respectively, to construct different Lyapunov-Krasovskii Functionals for each subinterval, and to obtain a weak conservative stability criterion by using the cross-convex combination technique. Finally, a numerical example is given to show the validity of the conclusions obtained in this paper. (2) the synchronization stability of neutral time-delay coupled complex systems is studied. First, the problem of synchronization stability is transformed into the stability analysis of zero solution of synchronization error. Then the time-delay interval is divided into two sub-regions, and the useful information of time-varying delays is fully considered, and different Lyapunov-Krasovskii functional is selected for each subinterval. Finally, the method of combining the technique of cross-convex combinatorial inequalities and the freedom matrix is combined. A delay-dependent synchronization stability criterion with lower conservatism is obtained. A numerical example is given to verify the weak conservatism of the results. When the network can not achieve synchronization by its own coupling, the synchronization control problem of neutral time-delay coupled complex networks is studied. Applying a simple linear feedback controller to the network nodes, the synchronization control problem is transformed into the stability analysis problem of the error system, and the synchronization stability criterion is obtained by using the time-delay decomposition method. The minimum controller gain can be obtained by solving linear matrix inequalities. Numerical simulation examples show that the conclusion is correct.
【学位授予单位】：太原科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5;O231

【参考文献】