时滞动力学系统的L-K稳定性条件分析

张晓艳 1; 3; 孙建桥 2; 丁千 1

doi:10.7652/xjtuxb201305013

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时滞动力学系统的L-K稳定性条件分析

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- 时滞动力学系统的L-K稳定性条件分析
- Analysis of Lyapunov-Krasovskii Stability for Dynamical Systems with Time Delay
- 西安交通大学学报 2013年47卷第5期页码：72-76
- 作者机构：
  
  1. 天津大学力学系,天津,300073
  2. 天津电子信息职业技术学院电子系,天津,300132
- 作者简介：
- 基金信息：
  
  : 2012-09-15。作者简介: 张晓艳(1974—),女,博士生;孙建桥(通信作者),男,教授,博士生导师。基金项目: 国家自然科学基金资助项目(11172197)
- DOI：10.7652/xjtuxb201305013
  中图分类号： O317
- 网络首发：2013-05-10，
  
  纸质出版：2013
- 稿件说明：
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张晓艳 1, 3, 孙建桥 2, 等. 时滞动力学系统的L-K稳定性条件分析[J]. 西安交通大学学报, 2013,47(5):72-76.

Analysis of Lyapunov-Krasovskii Stability for Dynamical Systems with Time Delay[J]. 2013, 47(5): 72-76.
张晓艳 1, 3, 孙建桥 2, 等. 时滞动力学系统的L-K稳定性条件分析[J]. 西安交通大学学报, 2013,47(5):72-76. DOI： 10.7652/xjtuxb201305013.

Analysis of Lyapunov-Krasovskii Stability for Dynamical Systems with Time Delay[J]. 2013, 47(5): 72-76. DOI： 10.7652/xjtuxb201305013.

摘要

针对线性时滞动力学系统的稳定性问题

比较了3种Lyapunov-Krasovskii(L-K)泛函。以一个在时滞PD反馈控制下的二阶线性系统作为数值实例

在反馈增益的参数空间中

根据不同的L-K泛函所对应的线性矩阵不等式条件计算线性系统的稳定域

并与由特征方程计算出的结果进行比较。结果表明:L-K泛函的稳定性条件是充分且保守的; Gu的完整L-K泛函的LMI不等式中暗含无穷多的矩阵

因此保守性得到很大改善

但其计算量显著增大; 当将Lyapunov稳定性理论用于控制设计时

经常使用保守的稳定性条件

但Gu的L-K泛函更有利于控制器设计。

Abstract

Three Lyapunov-Krasovskii(L-K)functionals for stability of time-delayed linear dynamical systems are compared. A benchmark second order linear system under delayed PD feedback controls is considered. The stability domains in the feedback gain parameter space are computed from the LMIs of different L-K functionals

and are compared with that calculated from the characteristic equation of the linear system. The results show that while most L-K functionals provide sufficient conditions for stability

which are conservative

Gu's complete L-K functional is the least conservative and the most accurate

and provides a necessary and sufficient condition for stability. Gu's complete L-K functional involves implicitly infinite number of matrices

hence

with a huge computational effort. When the Lyapunov stability theory is adopted for control design

the conservative stability conditions may be used

while Gu's complete L-K functional is more favorable to the design of controller.

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references

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