非线性时滞系统实用稳定性的Liapunov－Razumikhin方法

Liapunov-Razumikhin Method for Practical Stability of Nonlinear Delay Systems

研究非线性时滞系统关于Ｅｕｃｌｉｄ空间Ｒｎ中子集的实用稳定性问题。利用Ｒａｚｕｍｉｋｈｉｎ方法建立由常微分方程描述的比较系统，由此根据比较原理得到由Ｖ函数表述的一般形式的实用稳定性条件，并讨论了时滞系统与其常微分比较系统在实用稳定性方面的关系。对于具有分离变量形式的比较系统，得到了更为具体的结果，另外还初步探讨了不需求解比较系统而进行检验的直接判据。最后给出示例说明文中主要结果。

This paper investigates practical stability of nonlinear delay systems withrespect to subsets of Euclid space R￣n.By virtue of Razumikhin approach comparisonsystem described by ordinary differential equations are intfodueed.Based on it genemlcriteria of practical stability in terms of V funoion are established according tocomparison principles.The relationship between practical stability of delay system andthat of its ordinary differential comparison system is discussed. More detailedconditions of practical stability are given in the case of comparison system withseparated variables.Besides two kinds of direct criteria that do not require knowledgeof solving comparison system are proposed. Finally, illustrative examples are workedout.