关于Lyapunov稳定性若干定理的推广  

The Generalization of Theorems about Lyapunov Stability Theory

作　　者：高莲[1] 包曙红[2] 

机构地区：[1]内蒙古农业大学理学院,内蒙古呼和浩特010018 [2]内蒙古工业大学电力学院,内蒙古呼和浩特010080

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2006年第4期407-412,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

摘　　要：利用两个推广的积分不等式,对Lyapunov函数中的限制条件做了改进,得到非自治矢量微分方程零解的稳定性、渐近稳定性及一致稳定性的充分性定理,推广了扰动微分方程组零解稳定性的若干判定定理.By using two generalized integral inequalities,the limitation conditions of Lyapunov function were improved. Sufficient theorems of stability, asymptotic stability and uniformly stability for zero solution of the non-autonomous vector differential equation were obtained, and certain criteria theorems of the disturbing differential equations were extended.

关 键 词：LYAPUNOV函数 稳定 渐近稳定 一致稳定 

分 类 号：O175.54[理学—数学]