引用本文:刘艳红,李春文,王玉振,吴热冰,楚冰.Lipschitz广义非线性系统观测器设计[J].控制理论与应用,2007,24(2):205~209.[点击复制]
LIU Yan-hong,LI Chun-wen,WANG Yu-zhen,WU Re-bing,CHU Bing.Observer design for Lipschitz nonlinear singular systems[J].Control Theory and Technology,2007,24(2):205~209.[点击复制]
Lipschitz广义非线性系统观测器设计
Observer design for Lipschitz nonlinear singular systems
摘要点击 2160  全文点击 1090  投稿时间：2005-07-11  修订日期：2006-05-15
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DOI编号  10.7641/j.issn.1000-8152.2007.2.008
  2007,24(2):205-209
中文关键词  广义非线性系统  观测器设计  渐近稳定  奇异值
英文关键词  nonlinear singular systems  observer design  ~asymptotical stability  singular value
基金项目  国家自然科学基金资助项目(69774011,60433050).
作者单位
刘艳红,李春文,王玉振,吴热冰,楚冰 郑州大学 电气工程学院, 河南 郑州 450001
清华大学 自动化系,北京100084
山东大学控制科学与工程学院,山东 济南 250061
普林斯顿大学Frick实验室,美国 普林斯顿 NJ08544 
中文摘要
      研究一类广义非线性系统的观测器设计问题.首先讨论了半正定Lyapunov函数下指数1广义非线性系统稳定及渐近稳定性,~然后对一类由线性和Lipschitz非线性项组成的广义非线性系统,给出了渐近稳定观测器存在的条件,~并把观测器反馈增益矩阵的设计归结为广义线性系统容许控制以及奇异值计算问题,~证明了若容许广义线性系统矩阵的最小奇异值大于系统的Lipschitz常数,容许控制器增益矩阵就是待求的观测器反馈增益矩阵.
英文摘要
      The observer design for nonlinear singular systems is discussed. First, for an index-one nonlinear singular systems, the stability and asymptotical stability with positive semi-definite Lyapunov functions are analyzed. Then, for nonlinear singular systems composed of linear and Lipschitz nonlinear terms, some sufficient conditions are proposed for the existence of asymptotically stable observer system. An algorithm is developed to calculate the observer gain, converting the original problem into admissible control of a linear singular system and the calculation of minimum singular value of the correspondingly closed system. It is proven that if the minimum singular value is greater than the Lipschitz constant of the nonlinear singular system, the admissible controller gain can serve as the observer gain.