Volume 27 Issue 3
Mar.  2001
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PENG Lin-ping. Strong Stability with Respect to Part of the Variablesin Systems with Impulse Effect[J]. Journal of Beijing University of Aeronautics and Astronautics, 2001, 27(3): 365-368. (in Chinese)
Citation: PENG Lin-ping. Strong Stability with Respect to Part of the Variablesin Systems with Impulse Effect[J]. Journal of Beijing University of Aeronautics and Astronautics, 2001, 27(3): 365-368. (in Chinese)

Strong Stability with Respect to Part of the Variablesin Systems with Impulse Effect

  • Received Date: 21 Jan 2000
  • Publish Date: 31 Mar 2001
  • The present paper introduces a new kind of stability——strong stability with respect to part of the variables in systems with impulse effect. The question on the stability is discussed. Effective sufficient conditions are found for strong stability with respect to partial variables of the zero solution of an impulsive differential system. The approach present is based on the specially introduced piecewise continuous Lyapunov functions and two important lemmas. Finally the obtained criteria are applied to the investigation of strong stability of the zero solutions with respect to part of the variables in impulsive differential systems.

     

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  • [1] Lakshmikantham V, Bainov D D, Simeonov P S. Theory of impulsive differential equations[M]. London:World Scientific Press, 1989. [2] Myshkis A D, Samoilenko A M. Systems with impulses in prescribed moments of time[J]. Math Sb,1967,74:202~208. [3] Samoilenko A M, Perestyuk N A. Stability of solutions of differential equations with impulse effect[J]. Differentsial-nye Uravneniya,1997,13:1981~1992. [4] Samoilenko A M, Perestyuk N A. On the stability of the solutions of systems with impulse effect[J]. Differentsial'nye Uravneniya,1981,17:1995~2001. [5] Simeonov P S, Bainov D D. Stability under persistant disturbances for systems with impulse effect[J]. J Math Anal Appl,1985,109(2):546~563. [6] 廖晓昕.稳定性的数学理论及应用[M].武汉:华中师范大学出版社,1988. [7] 徐道义.稳定性理论中几个基本定理的推广[J]. 应用数学, 1992,2:76~80. [8] 彭临平.具有线性扰动的线性脉冲微分系统的有界增长[J].高校应用数学学报,1995,10A(2):167~172.
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