华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (3): 31-38.

• 数学 统计学 • 上一篇    下一篇

差分方程的两度量稳定和扰动锥值Lyapunov函数（英）

耿凤杰   

  1. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2005-09-20 修回日期:2006-03-19 出版日期:2007-05-25 发布日期:2007-05-25
  • 通讯作者: 耿凤杰

Stability in Terms of Two Measures with Perturbing Lyapunov Functions(English)

GENG Feng-jie   

  1. epartment of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2005-09-20 Revised:2006-03-19 Online:2007-05-25 Published:2007-05-25
  • Contact: GENG Feng-jie

摘要： 将扰动锥值 Lyapunov 函数方法引入差分方程; 在较弱的条件下讨论了差分方程两度量稳定 ($(h_0,h)$-稳定)和两度量渐近稳定 ($(h_0,h)$-渐近稳定 )等性质.

关键词: $\phi_0$-稳定, 一致 $\phi_0$-稳定, $(h_0, h)$-稳定, $(h_0, h)$-渐近稳定, $\phi_0$-稳定, 一致 $\phi_0$-稳定, $(h_0, h)$-稳定, $(h_0, h)$-渐近稳定

Abstract: This paper extended the method of perturbing cone-valued Lyapunov functions for a system of difference equations. Some properties of $(h_0,h)$-stability and $(h_0,h)$-asymptotical stability were discussed under much weaker assumptions.

Key words: uniformly $\phi_0$-stable, $(h_0, h)$-stable, $(h_0, h)$-asymptotically stable, \phi_0$-stable, uniformly $\phi_0$-stable, $(h_0, h)$-stable, $(h_0, h)$-asymptotically stable

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