| 引用本文: | 邱宏凌,沈俊.分数阶时滞锥不变系统的稳定性和增益性能[J].控制理论与应用,2026,43(3):471~479.[点击复制] |
| QIU Hong-ling,SHEN Jun.Stability and gain performance of fractional-order delayed cone-invariant systems[J].Control Theory & Applications,2026,43(3):471~479.[点击复制] |
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| 分数阶时滞锥不变系统的稳定性和增益性能 |
| Stability and gain performance of fractional-order delayed cone-invariant systems |
| 摘要点击 650 全文点击 99 投稿时间：2024-03-28 修订日期：2025-10-22 |
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| DOI编号 10.7641/CTA.2024.40177 |
| 2026,43(3):471-479 |
| 中文关键词 分数阶正系统 锥不变性 锥诱导增益 无界时滞 |
| 英文关键词 fractional-order positive system cone invariance cone-induced gain unbounded delays |
| 基金项目 国家自然科学基金项目(61973156),江苏省研究生科研与实践创新计划项目(KYCX24 0593)资助. |
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| 中文摘要 |
| 本文主要分析具有锥不变性和无界时滞的分数阶线性系统的稳定性和输入输出增益.这类系统的轨迹通
常被限制在一个正则锥里面,是分数阶时滞正系统的一种推广形式.首先,利用系统状态方程的解的轨迹,一个保
证其锥不变性的充要条件被给出.根据正则锥上的偏序关系,给出了保证分数阶锥不变时滞系统的稳定性的充要条
件. 该方法同样适用于系统在无时滞下的情形,这意味着分数阶时滞锥不变系统的稳定性对时滞的大小不敏感;此
外, 通过取整函数来构造一个采样系统并分析其状态轨迹与无时滞副本系统的状态轨迹偏序关系,从而以系统矩阵
的形式给出分数阶输入输出锥不变系统的锥诱导增益的刻画;最后,提供一个数值例子来说明理论结果. |
| 英文摘要 |
| This paper mainly studies the stability and input-output gain of fractional-order linear systems with cone
invariance and unbounded time-varying delays. The trajectories of such systems are usually restricted in a proper cone,
which is a generalization of fractional-order delayed positive systems. Firsly, using the trajectory of the solution of the
system state equation, a necessary and sufficient condition that ensures the cone invariance of the system is given. According
to the partial order relationship on a proper cone, a necessary and sufficient condition that ensures the asymptotic stability
of fractional-order cone-invariant delayed system is given. The method is also applicable to the case when the system
without delays, which means that the stability of fractional-order cone-invariant systems is not sensitive to the size of
delays. Moreover, through the construction of a sampling system using rounding functions and the analysis of the partial
order relationship between state trajectories of the sampling system and their corresponding counterparts without delays,
the cone-induced gain of fractional-order cone-invariant systems is characterized in terms of system matrices. Finally, a
numerical example is provided to illustrate the theoretical results. |
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