| 引用本文: | 王其祥,龙飞,莫立坡,杨靖.Caputo分数阶切换线性系统的指数稳定性[J].控制理论与应用,2023,40(2):304~312.[点击复制] |
| WANG Qi-Xiang,LONG Fei,MO Li-Po,YANG Jing.Exponential stability of Caputo fractional order switched linear system[J].Control Theory and Technology,2023,40(2):304~312.[点击复制] |
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| Caputo分数阶切换线性系统的指数稳定性 |
| Exponential stability of Caputo fractional order switched linear system |
| 摘要点击 1316 全文点击 430 投稿时间：2021-09-26 修订日期：2022-09-11 |
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| DOI编号 10.7641/CTA.2022.10910 |
| 2023,40(2):304-312 |
| 中文关键词 Caputo分数阶切换线性系统 多Lyapunov函数 模型依赖平均驻留时间 指数稳定性 |
| 英文关键词 Caputo fractional order switched linear system multiple Lyapunov functions model-dependent average dwell time exponential stability |
| 基金项目 国家自然科学基金项目(61813006, 61973329), 贵州省基础研究计划重点项目(20191416), 贵州省教育厅创新群体(黔教合KY字[2021]012), 贵州 省科技基金(黔科合基础[2020]1Y266), 贵州省工业攻关项目(黔科合支撑[2019]2152), 物联网理论与应用案例库(KCALK201708)资助. |
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| 中文摘要 |
| 众所周知, 与整数阶切换系统不同, Caputo分数阶切换系统的积分下界不能随子系统的切换而被更新, 意
味着在下界非一致的任意区间内不能直接取分数阶导数的分数阶积分. 对此, 本文给出了一个不等式(文中引理6)
克服这一问题, 并用1个数值例子进行了验证. 通过这一不等式, 然后分别利用多Lyapunov函数方法和模型依赖平
均驻留时间(MDADT)方法, 给出了Caputo分数阶切换线性系统指数稳定的条件, 并利用2个数值例子进行验证. |
| 英文摘要 |
| As we all know, different from the integer order switched systems, the integral lower bound of Caputo
fractional order switched systems cannot be updated with the switching of subsystems, which means that the fractional
integral of fractional derivative cannot be taken directly in any interval with non-uniform lower bound. In order to overcome
the above problem, an inequality (Lemma 6) is given in this paper. Through this inequality, the sufficient condition for the
exponential stability of Caputo fractional order switched linear systems is given by using the multiple Lyapunov function
and the model-dependent average dwell time (MDADT) method, respectively. Finally, two number examples are provided
to verify the results. |
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