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二阶时滞微分方程的脉冲指数稳定性 被引量：1

Impulsive Stability for Second-order Differential Equation with Delay
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摘要 研究二阶时滞微分方程的脉冲控制,利用Lyapunov函数方法,得到了二阶时滞微分方程的脉冲指数稳定的充分条件,推广、改进了相关文献的结果,举例说明了脉冲的控制作用. This paper is concerned with impulsive control of second order delay differential equation. By employing the method of Lyapunov functions, criteria on the exponential stabilization by impulses are gained. Our results generalize and improve that in the relative literatures. An example is also given to illustrate the efficiency of our result,in which the control effects of impulses are especially stressed.
作者 廖成斌 赵立春
机构地区 兰州理工大学计算机与通信学院 兰州理工大学理学院
出处 《兰州交通大学学报》 CAS 2009年第1期157-160,共4页 Journal of Lanzhou Jiaotong University
基金 甘肃省自然科学基金(3ZS062-B25-019)
关键词 时滞 脉冲 稳定性 LYAPUNOV函数 delay impulse stability Lyapunov function
分类号 O175.13 [理学—基础数学]
  • 相关文献

参考文献7

  • 1Wang feng. Impulsive stabilization of second order differential equation[J]. South China Normal Univ. Nature. Sci. Ed. 2001(1):16-19.
  • 2Shen J, Luo Z, Liu X. Impulsive stabilization of functional differential equations via liapunov funetional[J]. Math. Anal. Appl, 1999,240:1-5.
  • 3Li X. Impulsive stabilization of linear differential system[J]. South China Normal Univ. Natur. Sci. Ed, 2002(1) :52-56.
  • 4Gimenes L P, Federson M. Existence and impulsive stability for second order retarded differential equations[J]. Appl. Math. Comput, 2006,177:44-62.
  • 5Weng A Z, Sun J T. Impulsive stabilization of secondorder delay differenlial equations[J]. Nonlinear Anal,2007(8):1410-1420.
  • 6Li X, Weng P. Impulsive stabilization of two kinds of second-order linear delay differential equations [J]. Math. Anal. Appl, 2004,291: 270-281.
  • 7程超,杜明银,栗永安.具密度依赖和脉冲生育的单种群阶段结构模型[J].甘肃科学学报,2008,20(3):23-26. 被引量：2

二级参考文献6

共引文献1

同被引文献8

  • 1Dingheng Pi. On the stability of a second order retarded differential equation [J].Applied Mathematics and Com- putation, 2015,256 : 324-333.
  • 2Guiling Chen, Onno van Gaans, Sjoerd Verduyn Lunel. Asymptotic behavior and stability of second order neutral delay differential equationsl-J]. Indagationes Mathemati- cae, 2014,25 : 405-426.
  • 3Leonid Berezansky, Alexander Domoshnitsky, Mikhail Gitman,Valery Stolbov. Exponential stability of a second order delay differential equation without damping term [J]. Applied Mathematics and Computation, 2015,258: 483-488.
  • 4Xiang Li, Peixuan Weng. Impulsive stabilization of two kinds of second-order linear delay differential equations[J].J Math Anal Appl,2004,291:270-281.
  • 5Aizhi Weng, Jitao Sun. Impulsive stabilization of second- order delay differential equations[J]. Nonlinear Analysis: Real World Applications, 2007,8 : 1410-1420.
  • 6L P Gimenes, M Federson. Existence and impulsive stabili- ty for second order retarded differential equations[J]. Ap- plied Mathematics and Computation, 2006,177 : 44-62.
  • 7黄灿云,赵立春,赵闽.一类二阶时滞微分方程的脉冲指数稳定性[J].甘肃科学学报,2009,21(2):10-13. 被引量：1
  • 8王宗毅.一类二阶时滞微分方程脉冲解的存在性与指数稳定性[J].华南师范大学学报（自然科学版）,2013,45(3):22-27. 被引量：1

引证文献1

兰州交通大学学报
2009年 第1期

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