输入带有时滞的线性系统的镇定

支霞, 冯红银萍

系统科学与数学 ›› 2021, Vol. 41 ›› Issue (1) : 17-23.

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PDF(360 KB)
系统科学与数学 ›› 2021, Vol. 41 ›› Issue (1) : 17-23. DOI: 10.12341/jssms14093
论文

输入带有时滞的线性系统的镇定

    支霞1,冯红银萍2
作者信息 +

Stabilization of a Linear System  with Input Delay

    ZHI Xia1 ,FENG Hongyinping2
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文章历史 +

摘要

考虑带有输入时滞的线性系统的镇定问题. %讨论一类带有输入时滞的线性系统的镇定问题. 通过把时滞写成一阶传播方程, 带有输入时滞的镇定问题转化为常微分方程和一阶双曲方程组成的串联系统的镇定问题. 与现有Backstepping 方法不同, 文章给出了新的变换, 其核函数是一阶倒向向量值常微分方程, 这使得控制的设计更加简单. 文章给出了新的状态反馈控制器, 并证明了闭环系统解的适定性和指数稳定性. 数值模拟说明, 给出的方法是非常有效的.

Abstract

In this paper, we consider stabilization of a linear system with input delay. By writing the time delay as a transport equation, the stabilization of linear system with time delay is converted into stabilization of a cascade system of a first order hyperbolic equation and an ordinary differential equation. Different from the Backstepping method, the kernel function of the proposed transformation is the first order backward vector-valued ordinary differential equation which simplifies the controller design. A new state feedback controller is given and the well-posedness and the exponential stability are proved. The numerical simulation illustrates that the propose method is quite effective.

关键词

Backstepping 变换 / 传播方程 / 输入时滞 / 指数稳定.

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支霞 , 冯红银萍. 输入带有时滞的线性系统的镇定. 系统科学与数学, 2021, 41(1): 17-23. https://doi.org/10.12341/jssms14093
ZHI Xia , FENG Hongyinping. Stabilization of a Linear System  with Input Delay. Journal of Systems Science and Mathematical Sciences, 2021, 41(1): 17-23 https://doi.org/10.12341/jssms14093
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