时滞系统的实用稳定性和Liapunov稳定性  

PRACTICAL StABILITY AND LIAPUNOV STABILITY OF DELAY SYSTEMS

作　　者：楚天广[1] 王照林[1] 

机构地区：[1]北京大学力学系,清华大学工程力学系

出　　处：《力学学报》1996年第2期200-206,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金;高等学校博士学科点专项科研基金

摘　　要：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．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.

关 键 词：时滞系统 实用稳定性 稳定性 李雅普诺夫 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]