时滞系统的实用稳定性和Liapunov稳定性

本文主要研究非线性时滞系统在两种度量下的实用稳定性问题．首先引入一类Ｒａｚｕｍｉｋｈｉｎ型微分比较原理和单调性准则，在此基础上提出一种Ｌｉａｐｕｎｏｖ－Ｒａｚｕｍｉｋｈｉｎ型直接方法，建立一般形式的实用稳定性直接判据．这些判据将问题约化为一组有限维的微分或积分不等式，可以直接根据系统方程进行检验，便于实际应用．然后利用这些结果研究时滞系统的Ｌｉａｐｕｎｏｖ稳定性．最后示例说明本文主要结果．

PRACTICAL StABILITY AND LIAPUNOV STABILITY OF DELAY SYSTEMS

This paper deals mainly with practical stability in terms of two measures for nonlinear systems with finite time delay.First,a kind of Ruzumikhin type differential comparison principle and monotone criterion are introduced. Then, based on them a Liapunov- Razumikhin direct method is presented, which results in general direct criteria of pactical stabilty.These criteria reduce the problem to a set of finite dimensional differential or integral inequlities and can be verified directly according to equations of the concerned system,and therefore are convenient for practical use.Also,the Liapunov stability of delay systems is considered by the proposed method.Finally,an illustrative example is woked out.