TANG Xiaowei,SUN Xiaohui.Stability of functional differential system with state-dependent impulses[J].Journal of Yanbian University,2014,40(04):299-304.
具依赖状态脉冲的泛函微分系统的稳定性
- Title:
- Stability of functional differential system with state-dependent impulses
- 关键词:
- (h0; h)-一致渐近稳定; 依赖状态脉冲; Lyapunov函数
- 分类号:
- O175.13
- 文献标志码:
- A
- 摘要:
- 利用Lyapunov函数结合Razumikhin技巧给出了在解曲线与每个脉冲面可连续碰撞有限次的情况下具依赖状态脉冲的无穷延滞型泛函微分系统稳定性的直接结果,改进和推广了文献[15-17]的结论.
- Abstract:
- In the case that the solution of one functional differential system with state-dependent impulses can beat each impulse surface finite times, we give the stable properties by Lyapunove functions and Razumikhin conditions, which improves the existing results.
参考文献/References:
[1] 傅希林,闫宝强,刘衍胜.脉冲微分系统引论[M].北京:科学出版社,2005.
[2] 傅希林,闫宝强,刘衍胜.非线性脉冲微分系统[M].北京:科学出版社,2008.
[3] 傅希林,范进军.非线性微分方程[M].北京:科学出版社,2010.
[4] Yan Baoqiang, Fu Xilin. Existence of solution for impulsive functional differential equations with infinite delay[J]. Chin Sci Abs, 1999,5(12):1497-1498.
[5] Lakshmikantham V, Liu Xinzhi. Stability analysis in terms of two measures[M]. Singapore: World Scientic, 1993.
[6] Zhang Yu, Sun Jitao. Strict stability of impulsive functional differential equations[J]. Math Anal Appl, 2005,301(1):237-248.
[7] Zhang Shunian. A new approach to stability theory of infinite delay differential equations[J]. Comput Math Appl, 2002,44(10):1275-1287.
[8] Luo Zhiguo, Shen Jianhua. Stability of functional differential equations with infinite delays[J]. Appl Math B, 2005,20(2):142-150.
[9] Luo Zhiguo, Shen Jianhua. Stability and boundedness results for impulsive functional differential equations with infinite delays[J]. Nonlinear Anal, 2001,46(4):475-493.
[10] Zhang Yu, Sun Jitao. Stability of impulsive infinite delay differential equations[J]. Appl Math Lett, 2006,19(10):1100-1106.
[11] 窦家维,李开泰.一类脉冲微分方程零解的稳定性[J].系统科学与数学,2004,24(1):56-63.
[12] 张瑜,王春燕,孙继涛.具有可变脉冲点的脉冲微分方程的稳定性[J].数学物理学报,2005,25(6):777-783.
[13] 罗宏,蒲志林,陈光淦.具有可变脉冲扰动的时滞脉冲微分方程解的稳定性[J].四川师范大学学报,2002,25(6):18-21.
[14] Kaul S. Vector Lyapunov functions in impulsive variable-time differential system[J]. Nonlinear Anal,1997,30(5):2695-2698.
[15] Liu Xinzhi, Wang Qing. Stability of nontrivial solution of delay differential equations with state-dependent impulses[J]. Appl Math Comput, 2006,174(1):271-288.
[16] Wang Lin, Fu Xilin. A new comparison principle for impulsive differential systems with variable impulsive perturbations and stability theory[J]. Comput Math Appl, 2007,54:730-736.
[17] Tang Xiaowei, Fu Xilin.New comparison principle with Razumikhin condition for impulsive infinite delay differential systems[J]. Discrect and Continuous Dynamical Systems-Supplement, 2009:739-743.
备注/Memo
收稿日期: 2014-06-27 作者简介: 唐晓伟(1983—),女,讲师,研究方向为微分方程稳定性.基金项目: 山东省优秀中青年科学家科研奖励基金资助项目(BS2012DX039); 国家自然科学基金资助项目(11301308)