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一类非线性动力系统实用稳定域的研究及应用 被引量：2

Study on Practical Stability Domain Estimates of a Class of Nonlinear Dynamical System with Application
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摘要 借助于李雅普诺夫函数讨论了一类非线性动力系统的实用稳定性和实用稳定域的估计问题,得到了实用稳定域存在的充分条件,给出了一类动力系统实用稳定域的具体形式.通过具体实例说明了所给条件的实用性,改进了已有的结果. In this paper, the practical stability and the estimates of practical stability domains of some nonlinear dynamical system are discussed by Lyapunov function, some sufficient conditions of the existence of domain of practical stability are given, and the method of constructing practical stability domains of a kind of dynamical system are obtained, which improved the result in the proceeding literature.
作者 杨玉华
机构地区 华北电力大学数理系
出处 《数学的实践与认识》 CSCD 北大核心 2012年第13期189-192,共4页 Mathematics in Practice and Theory
关键词 动力系统 实用稳定 实用稳定域 实用稳定域估计 李雅普诺夫函数 practical stability practical stability domains estimates of practical stabilitydomains V-function
分类号 O19 [理学—基础数学]
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参考文献8

  • 1玛尔德纽克,孙振奇著.实用稳定性及应用[M].科学出版社,2005.
  • 2王照林.运动稳定及其应用[M].北京高等教育出版社,1992.
  • 3Lakshmikantham V, Leela S, Martynyuk A A. Practical Stability of Nonlinear Systems[M]. Singa- pore:World Scientific, 1990.
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  • 7Zhang Yu, Sun Jitao. Eventual practical stability of impulsive differential equations with time delay in terms of two measurements[J]. Journal of Computational and Applied Mathematics, 2005(176): 223-229.
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同被引文献14

  • 1冯伟贞.线性时变脉冲切换系统稳定性[J].华南师范大学学报（自然科学版）,2006,38(3):12-18. 被引量：3
  • 2LIU X Z. Practical stabilization of control systems with impulse effects[ J ]. Journal of Mathematical Analysis and Applications, 1992, 166(2) : 563 -576.
  • 3KUIAVA R, RAMOS R A, POTA H R, et al. Practical stability of switched systems without a common equilibria and governed by a time-dependent switching signal[J]. European Journal of Control, 2013, 19(3) : 206 -213.
  • 4MITROPOLSKIY Y A, IOVANE G, BORYSENKO S D. About a generalization of Bellman - Bihari type inequalities for discontinu- ous functions and their applications[ J]. Nonlinear Analysis: The- ory, Methods & Applications, 2007, 66 (10) : 2140 - 2165.
  • 5Chen Wuhua, Zheng Weixing. Exponential stability ot nonlinear time-delay system with delayed impulse effects[J]. Automatica, 2011, 47(5): 1075-1083.
  • 6Mohamad S Alwan, Xinzhi Liu. Stability of singularly perturbed switched systems with time delay and impulsive effects[J]. Nonlinear Analysis: Theory, Methods Appl, 2009, 71(9): 4297-4308.
  • 7Liu Yubin, Feng Weizhen. Razumikhin- Lyapunov functional method for the stability of impulsive switched systems with time delay[J]. Math Comput Model, 2009, 49: 249-264.
  • 8Liu Xinzhi. Practical Stabilization of Control Systems with Impulse Effects[J]. J Math Anal Appl, 1992, 166: 563-576.
  • 9Li Shao'e, Feng Weizhen. Practical stability of linear switched impulsive system with time delay[J]. Electron J Diff Equ, 2014, 262: 1-21.
  • 10Wang Qing, Liu Xinzhi. Impulsive stabilization of delay differential systems via the Lyapunov-Razumikhin method[J]. Appl Math Lett, 2007, 20(8): 839-845.

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数学的实践与认识
2012年 第13期

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