中立型大系统的稳定性(英文)

STABILITY OF LARGE SCALE NEUTRAL FUNCTIONAL DIFFERENTIAL SYSTEMS

根据大系统分解集结的思想方法,利用比较原理和李雅普诺夫函数方法,分别讨论了中立型微分差分大系统和超中立型泛函微分大系统解的稳定性。通过分析低维子系统和关联项的结构,给出具有分解形式的大系统平凡解渐近稳定和一致稳定的充分条件。作为应用,还讨论了一类具有特殊形式的中立型大系统解的稳定性。

In this paper, two classes of neutral functional differential equations are considered. The decomposition-aggregation technique, comparison principle and vector Liapunov function method are used to discuss stability of large scale neutral systems. The objective is to consider neutral functional differential equations as large scale systems, and to analyse the stability of the large scale neutral systems in terms of their lower order subsystems and their interconnected structure. Some sufficient conditions such that the zero solution of the large scale systems is asymptotically stable and uniformly stable are obtained. An example is given to illustrate the obtained results.