期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

三阶系统族的共同二次Lyapunov函数 被引量：2

Common quadratic Lyapunov functions for third order systems
下载PDF
导出
摘要 研究了寻找三阶系统族的共同二次Lyapunov函数问题.针对给定的稳定的三阶系统提出了寻找二次Lyapunov函数集的方法,然后获得了三阶系统族具有共同二次Lyapunov函数的充分条件.该充分条件易于构造,从而具有较强的工程实用性.文中实例验证了所得结果的有效性. This paper considers the problemof finding a common quadratic Lyapunov function for a set of third order systems. Firstly, for a given stable third order system, the method to seek the set of quadratic Lyapunov functions is proposed, and then, a sufficient condition for a set of third order systems to share a common quadratic Lyapunov function is obtained. The proposed sufficient condition is easy to be constructed and applied. Finally, an example is given to verify the effectiveness of the obtained results.
作者 董亚丽 秦化淑
机构地区 天津工业大学理学院 中国科学院数学与系统科学研究院系统科学研究所
出处 《控制理论与应用》 EI CAS CSCD 北大核心 2006年第2期235-239,共5页 Control Theory & Applications
基金 天津市高等学校科技发展基金资助项目(20051527)
关键词 共同二次Lyapunov函数 正交变换 切换系统 common quadratic Lyapunov function （QLF） orthogonal transformation switched system
分类号 O231 [理学—运筹学与控制论]
  • 相关文献

参考文献8

  • 1AGRACHEV A A, LIBERZON D. Lie-algebraic stability criteria for switched systems [J]. SIAM J of Control Optimization,2001,40( 1 ):253 -270.
  • 2LIBERZON D, HESPANHA J P, MORSE A S. Stability of switched linear systems: a Lie-algebraric condition [ J]. Systems & Control Letters, 1999, 37 ( 3 ) : 117 - 122.
  • 3DAYAWANSA W, MARTIN C F. A converse Lyapunov theorem for a class of dynamical systems which undergo switching [ J ].IEEE Trans on Automatic Control, 1999, 44(4) :751 -760.
  • 4NARENDRA K S, BALAKRISHNAN J. A common Lyapunov function for stable LIT systems with commuting Amatrices [ J].IEEE Trans on Automatic Control, 1994,39(12) :2469 - 2471.
  • 5SUN Z, SHORTEN R. On convergence rates of switched linear systems [ C ] //Proc of the 42th IEEE Conf on Decision and Control. Maui, Hawaii: IEEE Press, 2003,5:4800-4805.
  • 6CHENG D, GUO L, HUANG J. On quadratic Lyapunov function[J].IEEE Trans on Automatic Control,2003,48(5) :885 -890.
  • 7YEDAVALLI R K, SPARKS A. Condition for the existence of a common Quadratic Lyapunov function via stability analysis of matrix families [ C]//Proc of American Control Conference. Anchorage, Alaska: IEEE Press, 2002: 1296- 1301.
  • 8LIBERZON D, TEMPO R. Common Lyapunov functions and gradient algorithms [J]. IEEE Trans on Automatic Control,2004, 49 (6) : 990 - 994.

同被引文献17

  • 1GAO Yan,LYGEROS J,QUINCAMPOIX M,et al. On the control of uncertain impulsive systems: approximate stabilization and controlled invariance[J]. International Journal of Control, 2004,77(16) : 1 393 - 1 407.
  • 2GAO Yan, YGEROS J,QUINCAMPOIX M. On the reachability problem of uncertain hybrid systems[J]. IEEE Transactions on Automatic Control, 2007, 52 (9):1 572 - 1 586.
  • 3DAYAWANSA W P, MARTIN C F.A converse Lyapunov theorem for a class of dynamical systems with undergo switching[J]. IEEE Transaction on Automatic Control,1999,44(4):751 - 760.
  • 4MANCILLA-AGUILAR J L, GARCIA R A. A converse Lyapunov theorem for nonlinear switched systems[J]. System and Control Letter, 2000,41 (1): 67 - 71.
  • 5CHEN Zheng,GAO Yan. The Computation of a common quadratic Lyapunov function for a linear system[J]. Journal of Information and Computing Science, 2007, 2 (4) :299 - 304.
  • 6CHENG D, GUO L, HUANG J. On quadratic lyapunov functions[J]. IEEE Transactions on Automatic Control, 2003,48(5) : 885 - 890.
  • 7MASON O, SHORTEN R. A result on the existence of common quadratic Lyapunov function for pairs of stable discrete-time LTI systems[C]//1Proceeding of the American Control Conference, Denver USA: 2003:4 471- 4 475.
  • 8Agrachev A A, Liberzon D. Lie-algebraic stability criteria for switched systems[J]. SIAM J of Control Optimiza tion,g001,40(1) :253-270.
  • 9Liberzon D, Hespanha J P, Morse A. Stability of switched linear systemsa Lie-algebraric condition[J]. Systems Control Letters, 1999,37(3) : 117-122.
  • 10Cheng D,Guo L, Huang J. On quadratic Lyapunov func- tion[J]. IEEE Transon Automatic Control, 2003,48(5): 885-890.

引证文献2

二级引证文献2

控制理论与应用
2006年 第2期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部