引用本文:丛屾, 费树岷, 徐君祥.时滞切换系统稳定性分析与镇定—Lyapunov函数方法[J].控制理论与应用,2007,24(3):465~470.[点击复制]
CONG Shen, FEI Shu-min, XU Jun-xiang.On stability analysis and stabilization of switched systems with delay–Lyapunov function approach[J].Control Theory and Technology,2007,24(3):465~470.[点击复制]
时滞切换系统稳定性分析与镇定—Lyapunov函数方法
On stability analysis and stabilization of switched systems with delay–Lyapunov function approach
摘要点击 2010  全文点击 1453  投稿时间：2005-04-04  修订日期：2006-02-23
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DOI编号  10.7641/j.issn.1000-8152.2007.3.026
  2007,24(3):465-470
中文关键词  切换系统  时滞  指数稳定性  Halanay型不等式
英文关键词  switched systems  time-delay  exponential stability  Halanay-type inequality
基金项目  国家自然科学基金资助项目(60574066)
作者单位
丛屾, 费树岷, 徐君祥 东南大学自动化研究所, 江苏南京210096
东南大学数学系, 江苏南京210096 
中文摘要
      利用Lyapunov函数方法克服“相空间”与“事件空间”之间的不一致, 以考虑时滞切换系统稳定性的分析与综合. 其一, 对将多Lyapunov函数方法推广至时滞情形, 由此给出子系统稳定性准则及切换序列的约束条件, 使整个系统是指数稳定的. 其二, 对于不稳定的时滞子系统, 提出了保证观测误差在任意切换作用下指数衰减的观测器设计方法, 并构造出基于估计状态的切换序列, 使状态变量指数收敛.
英文摘要
      Lyapunov function approach is introduced to investigate the stability of switched systems with delay for overcoming the discordance between the “phase space”and “event space”, and yields results both in analysis and synthesis. Firstly, the multiple Lyapunov functions approach is generalized for the case of time-delay, from which the stability criterion of subsystems and the constraint condition on switching sequence are established for preserving the exponential stability of the switched system. Secondly, for the unstable subsystems with delay, the state-observer is designed to guarantee the exponential decay of the estimation error undergoing arbitrary switching action, and the switching law is also constructed from the estimated state to make state variables be exponentially convergent to zero.