关于Lyapunov稳定性若干定理的推广

The Generalization of Theorems about Lyapunov Stability Theory

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.