退化时滞微分系统的特征根分布与指数稳定

该文首先研究了退化时滞微分系统的特征根分布, 指出如果退化时滞微分系统的所有特征根都具有负实部, 在一个条件下, 特征根的负实部的最大值为负.由此可以得到一个条件, 在该条件下如果所有特征根都具有负实部, 则退化时滞微分系统的解是指数稳定的.作为例子, 对中立型给出其解为指数稳定的条件.

Distribution of Characteristic Roots and Exponential Stability ofSingular Differential Delay Systems

This paper firstly investigates the distribution of the characteristic roots of singular differential systems with delay. It is pointed out that if all the characteristic roots have negative real parts, under a condition, the maximal value of real parts of the characteristic roots is negative. This result shows that if all the characteristic roots have negative real parts, under a condition, the solution of singular differential systems with delay is exponentially stable. And finally, as an example, for the neutral differential systems, the conditions are given under which the solution is exponentially stable.