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一类二阶时滞微分方程的脉冲指数稳定性 被引量：1

Impulsive Exponential Stabilization of a Class Second-order Differential Equation with Delay
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摘要 主要研究二阶时滞微分方程的脉冲控制,利用Lyapunov函数技巧,得到了加入适当脉冲使二阶时滞微分方程指数稳定的条件,并举例说明了脉冲的控制作用. The impulsive control of second-order differential equation is studied. By employing the method of Lyapunov functions, criteria in the exponential stabilization by impulses are gained,the paper generalizes and improves the results in the literature. An example is also given to illustrate the efficiency of our result, in which the control effects of impulses are especially stressed.
作者 黄灿云 赵立春 赵闽
机构地区 兰州理工大学理学院
出处 《甘肃科学学报》 2009年第2期10-13,共4页 Journal of Gansu Sciences
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 impulsiv stabilization Lyapunov function
分类号 O175.13 [理学—基础数学]
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参考文献8

  • 1Feng W. Impulsive Stabilization of Second Order Differential Equation[J]. South China Normal Univ. Natur. Sci.Ed. , 2001,1 :16-19.
  • 2Shen J, Luo Z, Liu X. Impulsive Stabilization of Functional Differential Equations Via Liapunov Functionals[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.
  • 4L P Gimenes, M Federson. Existence and Impulsive Stability for Second Order Retarded Differential Equations[J]. Appl. Math. Comput. 2006,177 : 44-62.
  • 5Weng A Z, Sun T. Impulsive Stabilization of Second-order Delay Differential Equations[J]. Nonlinear Anal. , 2007,8:1 410-1 420.
  • 6Li X, Weng P. Impulsive Stabilization of Two Kinds of Second-order Linear Delay Differential Equations[J]. Math. Anal. Appl. , 2004,191 :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
  • 8Li X, Weng P. Impulsive Stabilization of Two Kinds of Second-order Linear Delay Differential Dquations[J]. Math. Anal. Appl. , 2004, 291:270-281.

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廖成斌,赵立春.二阶时滞微分方程的脉冲指数稳定性[J].兰州交通大学学报,2009,28(1):157-160. 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

甘肃科学学报
2009年 第2期

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