引用本文:刘乾,何勇,宁重阳.时滞半Markov切换随机系统输入–状态稳定性分析的时变驻留时间条件方法[J].控制理论与应用,2023,40(2):322~330.[点击复制]
LIU Qian,HE Yong,NING Chong-yang.Approach of time-varying dwell time condition for the input-to-state stability analysis of the time-delayed stochastic systems with semi-Markovian switching[J].Control Theory and Technology,2023,40(2):322~330.[点击复制]
时滞半Markov切换随机系统输入–状态稳定性分析的时变驻留时间条件方法
Approach of time-varying dwell time condition for the input-to-state stability analysis of the time-delayed stochastic systems with semi-Markovian switching
摘要点击 874  全文点击 311  投稿时间：2021-12-31  修订日期：2022-09-11
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DOI编号  10.7641/CTA.2022.11309
  2023,40(2):322-330
中文关键词  半Markov切换系统  随机系统  时滞系统  输入–状态稳定性  Lyapunov-Razumikhin函数  不定多重Lyapu-nov函数  时变驻留时间条件
英文关键词  semi-markovian switched systems  stochastic systems  time-delayed systems  input-to-state stability  Lyapunov-Razumikhin functions  indefinite multiple Lyapunov functions  time-varying dwell time condition
基金项目  国家自然科学基金项目(61973284)资助.
作者单位E-mail
刘乾 中国地质大学(武汉） qliu96@cug.edu.cn 
何勇* 中国地质大学(武汉） heyong08@cug.edu.cn 
宁重阳 中南林业科技大学  
中文摘要
      本文针对时滞半Markov切换随机系统, 建立了一种基于时变驻留时间条件的不定多重Lyapunov-Razumik-hin函数方法, 给出了系统输入–状态稳定性和积分输入–状态稳定性判别条件. 一方面, 构造了一种不定多重Lyapu-nov函数, 不要求每个子系统对应的Lyapunov-Razumikhin函数导数总是保持负定, 从而放宽了对于子系统稳定性要 求, 甚至允许了不稳定子系统的存在; 另一方面, 提出了一种时变驻留时间条件来表示半Markov切换信号的切换次 数与子系统驻留时间之间的关系, 利用时变函数对切换次数进行估计, 间接放松了不定多重Lyapunov-Razumikhin 函数选取的限制. 最后, 数值算例验证了所提方法的有效性.
英文摘要
      The time-delayed stochastic systems with semi-Markovian switching are investigate in this paper. We establish an indefinite multiple Lyapunov-Razumikhin functions method based on a time-varying dwell time condition, and get input-to-state stability and integral input-to-state stability conditions. On the one hand, by introducing the indefinite multiple Lyapunov functions, we do not require that derivatives of Lyapunov-Razumikhin functions always remain negative, which eases stability requirements of subsystems, even allows unstable subsystems to exist. On the other hand, a time-varying dwell time condition is proposed to illustrate the connection between the switch counts and the dwell time. By this condition, we propose a time-varying functions to estimate the switch counts of the semi-Markovian switching signal, which mediately loosens the restrictions of multiple Lyapunov functions. Finally, a numerical example is presented to show the effectiveness of our results.