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时滞微分方程依照两种测度的稳定性 被引量:1

Stability Criteria in Terms of Two Measures for Delay Differential Equations
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摘要 运用变异Liapunov方法 ,讨论了时滞微分方程依照两种测度的稳定性· 借助于中间测度h (t,x) ,在未扰动系统为常微分方程的情形下 ,得到了关于时滞微分方程非一致和一致稳定性的判定定理· By using the variational Liapunov method, stability properties in terms of two measures for delay differential equations are discussed. In the case that the unperturbed systems are ordinary differential systems, employing auxiliary measure h *(t,x), criteria on nonuniform and uniform stability in terms of two measures for delay differential equations are established.
出处 《应用数学和力学》 EI CSCD 北大核心 2002年第3期283-291,共9页 Applied Mathematics and Mechanics
基金 国家自然科学基金资助项目 (198310 30 )
关键词 时滞微分方程 变异Liapunov方法 稳定性 测度 非一致稳定性 delay differential equations variational Lyapunov method stability two measures
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参考文献5

  • 1[1]Hale J. Theory of Differential Equations[M]. New York:Springer-Verlag,1977.
  • 2[2]LIU Xin-zhi. Advances in stability theory of nonlinear systems[A]. In:Proceedings of International Conference on Dynamical Systems and Differential Equations[C]. Vol E-3 Shanghai:Shanghai Jiaotong University Press,1998.
  • 3[3]Lakshmikantham V. Advances in UAS for functional differential equations[J]. Merm Diff Equas Math Phy,1997,12(1):131-134.
  • 4[4]Lakshmikantham V, Leela S, Sivasundaram S. Liapunov functions on product spaces and stability theory of delay differetnial equations[J]. J Math Anal Appl,1991,154(2):391-402.
  • 5[5]Lakshmikantham V. LIU Xin-zhi. Stability Analysis in Terms of Two Measures[M]. Singapore:World Scientific,1993.

同被引文献5

  • 1Hale J.Theory of functional differential equations[M].New York:Springer-Verlag,1977.
  • 2李森林,温立志.泛函微分方程[M].湖南:湖南科学出版社,1985.
  • 3Lakshmikantham V.,Liu Xinzhi & Leela S.,Variational Lyapunov method and stability theory[J].Mathematical Problem in Engineering,1998,(3):555-571.
  • 4Liu Xinzhi & Vatsala A.Variation of parameters in terms of Lyapunov-like functions and stability of perturbed systems[J].Nonlinear Studies,1998,(5):47-58.
  • 5Lakshmikantham V & Liu Xinzhi.Stability in terms of two measures[M].Singapore,World Scientific,1993.

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