引用本文:丛 屾,费树岷,李 涛.时滞切换系统指数稳定性分析: 微分不等式方法[J].控制理论与应用,2008,25(3):521~524.[点击复制]
CONG Shen,FEI Shu-min,LI Tao.On exponential stability of switched systems with time-delays: differential inequality approach[J].Control Theory and Technology,2008,25(3):521~524.[点击复制]
时滞切换系统指数稳定性分析: 微分不等式方法
On exponential stability of switched systems with time-delays: differential inequality approach
摘要点击 1629  全文点击 1417  投稿时间：2006-05-22  修订日期：2007-04-10
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DOI编号  10.7641/j.issn.1000-8152.2008.3.024
  2008,25(3):521-524
中文关键词  切换系统  时滞  指数稳定性  Halanay不等式
英文关键词  switched systems  time-delay  exponential stability  Halanay inequality
基金项目  国家自然科学基金资助项目(60574066).
作者单位
丛 屾 南京理工大学 自动化学院, 南京 江苏 210094 
费树岷 东南大学 自动化研究所, 南京 江苏 210096 
李 涛 东南大学 自动化研究所, 南京 江苏 210096 
中文摘要
      考虑由多个时滞系统组成的切换系统, 并研究在什么条件下, 可以把无时滞切换系统的稳定性分析及结论推广至上述的时滞系统. 方法是将时滞项作为线性常微分方程扰动项, 利用常数变易公式与Halanay微分不等式, 分析时滞项对于切换系统稳定性的影响. 结论表明, 在时滞项满足某些前提时, 切换系统稳定性分析的Lyapunov方法仍然适用. 仿真算例验证了方法的有效性.
英文摘要
      The switched system consisting of a family of subsystems with time-delays is considered. Our problem is to find the proper conditions, under which the methods and results in the stability studying of a switched system without time-delays can be generalized to the above system with time-delays. We treat the time-delay term as the perturbation of a linear ordinary differential equation, and exploit the variation-of-constants formula and Halanay differential inequality. The obtained results imply that the Lyapunov approach is still applicable for the stability analysis of switched systems with time-delays in some prescribed conditions. Finally, examples are given to demonstrate the proposed approach.