留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一类混杂动态系统的能控性(Ⅰ)——基本结果

谢广明 王龙 叶庆凯

谢广明, 王龙, 叶庆凯. 一类混杂动态系统的能控性(Ⅰ)——基本结果[J]. 应用数学和力学, 2003, 24(9): 919-928.
引用本文: 谢广明, 王龙, 叶庆凯. 一类混杂动态系统的能控性(Ⅰ)——基本结果[J]. 应用数学和力学, 2003, 24(9): 919-928.
XIE Guang-ming, WANG Long, YE Qing-kai. Controllability of a Class of Hybrid Dynamic Systems(Ⅰ)—Basic Properties and Preliminary Results[J]. Applied Mathematics and Mechanics, 2003, 24(9): 919-928.
Citation: XIE Guang-ming, WANG Long, YE Qing-kai. Controllability of a Class of Hybrid Dynamic Systems(Ⅰ)—Basic Properties and Preliminary Results[J]. Applied Mathematics and Mechanics, 2003, 24(9): 919-928.

一类混杂动态系统的能控性(Ⅰ)——基本结果

基金项目: 国家杰出青年科学基金资助项目(69925307);国家重点基础研究与发展计划基金资助项目(2002CB312200);中国博士后基金资助项目
详细信息
    作者简介:

    谢广明(1972- ),男,北京人,博士(后),研究方向为混杂切换系统、广义系统、时滞系统和网络控制系统(E-mail:xiegming@mech.pku.edu.cn).

  • 中图分类号: TP13;TP273;O317

Controllability of a Class of Hybrid Dynamic Systems(Ⅰ)—Basic Properties and Preliminary Results

  • 摘要: 首次将时滞现象引入到线性切换系统的模型中,研究含有时滞线性切换系统的能控性及其判定条件。全部工作由三部分组成,第Ⅰ部分首先,提出含时滞的线性切换系统的数学模型,并介绍切换系统的基本概念—切换序列。其次,引入列空间、循环不变子空间和广义循环不变子空间等基本几何概念,给出一些有关概念的基本性质,特别是分离引理。然后以一个基本引理的形式揭式某一积分方程的解集与广义循环不变子空间之间的联系,这个引理将在能控性的判定中起关键作用。这些概念和引理都将作为以后展开能控性分析所必需的研究工具。
  • [1] Liberzon A B,Morse A S.Basic problems in stability and design of switched systems[J].IEEE Contr Syst Mag,1999,19(5):59-70.
    [2] Ezzine J.Haddad A H.Controllability and observability of hybrid systems[J].Int J Control,1989,49(6):2045-2055.
    [3] SUN Zheng-dong,ZHENG Da-zhong.On reachability and stabilization of switched linear systems[J].IEEE Trans Automat Contr,2001,46(2):291-295.
    [4] 谢广明,郑大钟.一类混杂系统的能控性与能达性[A],见:秦化淑编.19届中国控制会议[C].香港:香港工程师协会,2000,114-117.
    [5] XIE Guang-ming,WANG Long.Necessary and sufficient conditions for controllability of switched linear systems[A].In:American Automatic Control Counci Ed.Proceedings of the Americal Control Conference 2002[C].USA:IEEE Service Center,2002,1897-1902.
    [6] XU Xu-ping,Antsaklis P J.On the reachability of a class of second-order switched systems[A].In:American Automatic Control Counci Ed.Proceedings of the American Control Conference 1999[C].USA:IEEE Service Center,1999,2955-2959.
    [7] Ishii H,Francis B A.Stabilization with control networks[J].Automatica,2002,38(10):1745-1751.
    [8] Ishii H,Francis B A.Stabilizing a linear system by switching control with dwell time[A].In:American Automatic Control Counci Ed.Proceedings of the American Control Conference 2001[C].USA:IEEE Service Center,2001,1876-1881.
    [9] Morse A S.Supervisory control of families of linear set-point controllers-Part1:Exact matching[J].IEEE Trans Automat Contr,1996,41(7):1413-1431.
    [10] Liberzon D,Hespanha J P,Morse A S.stability of switched systems:a Lie-algebraic condition[J].Systems Contr Lett,1999,37(3):117-122.
    [11] Hespanha J P,Morse A S.Stability of switched systems with average dwell-time[A].In:IEEE Control Systems Society Ed.Proceedings of the 38th Conference on Decesion and Control[C].USA:IEEE Customer Service,1999,2655-2660.
    [12] Narendra K S,Balakrishnan J.A common Lyapunov function for stable LTI systems with commuting A-matrices[J].IEEE Trans Automat Contr,1994,39(12):2469-2471.
    [13] Narendra K S,Balakrishnan J.Adaptive control using multiple models[J].IEEE Trans Automat Contr,1997,42(1):171-187.
    [14] Petterson S,Lennartson B.Stability and robustness for hybrid systems[A].In:IEEE Control Systems Society Ed.Proceedings of the 35th Conference on Decesion and Control[C].USA:IEEE Customer Service,1996,1202-1207.
    [15] YE Hong,Michel A N,HOU Ling.Stability theory for hybrid dynamical systems[J].IEEE Trans Automat Contr,1998,43(4):461-474.
    [16] HU Bo,XU Xu-ping,Antsaklis P J,et al.Robust stabilizing control laws for a class of second-order switched systems[J].Systems and Control Letters,1999,38(2):197-207.
    [17] Branicky M S.Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J].IEEE Trans Automat Contr,1998,43(4):475-482.
    [18] Shorten R N,Narendra K S.On the stability and existence of common Lyapunov functions for stable linear switching systems[A].In:IEEE Control Systems Society Ed.Proceedings of the 37th Conference on Decesion and Control[C].USA:IEEE Customer Service,1998,3723-3724.
    [19] Johansson M,Rantzer A.Computation of piecewise quadratic Lyapunov funtions for hybrid systems[J].IEEE Trans Automat Contr,1998,43(4):555-559.
    [20] Wicks M A,Peleties P,DeCarlo R A.Construction of piecewise Lyapunov funtions for stabilizing switched systems[A].In:IEEE Control Systems Society Ed.Proceedings of the 33th Conference on Decesion and Control[C].USA:IEEE Customer Service,1994,3492-3497.
    [21] Peleties P,DeCarlo R A.Asymptotic stability of m-switched systems using Lyapunov-like functions[A].In:American Automatic Control Counci Ed.Proceedings of the American Control Conference 1991[C].USA:IEEE Service Center,1991,1679-1684.
    [22] Chyung D H.Oh the controllability of linear systems with delay in control[J].IEEE Trans Autom Contr,1970,15(2):694-695.
    [23] Chyung D H.Controllability of linear systems with multiple delays in control[J].IEEE Trans Automat Contr,1970,15(6):694-695.
    [24] 黄琳.系统与控制中的线性代数[M].北京:科学出版社,1984.
  • 加载中
计量
  • 文章访问数:  2479
  • HTML全文浏览量:  112
  • PDF下载量:  765
  • 被引次数: 0
出版历程
  • 收稿日期:  2002-01-29
  • 修回日期:  2003-03-25
  • 刊出日期:  2003-09-15

目录

    /

    返回文章
    返回