Analysis of Lyapunov-Krasovskii Stability for Dynamical Systems with Time Delay

doi:10.7652/xjtuxb201305013

您当前的位置：

首页 >

文章列表页 >

Analysis of Lyapunov-Krasovskii Stability for Dynamical Systems with Time Delay

更新时间：2025-07-09

- Analysis of Lyapunov-Krasovskii Stability for Dynamical Systems with Time Delay
- Vol. 47, Issue 5, Pages: 72-76(2013)
- 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：
- DOI：10.7652/xjtuxb201305013
  CLC： O317
- Online First：10 May 2013，
  
  Published：2013
- 稿件说明：
移动端阅览
Analysis of Lyapunov-Krasovskii Stability for Dynamical Systems with Time Delay[J]. 2013, 47(5): 72-76.
DOI：

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.

关键词

Keywords

references

KAPILA V, HADDAD W M. Robust stabilization for systems with parametric uncertainty and time delay [J]. Journal of the Franklin Institute, 1999, 336: 473-480.

WU Hansheng, MIZUKAMI K. Robust stability criteria for dynamical systems including delayed perturbations [J]. IEEE Transactions on Automatic Control, 1995, 40(3): 487-490.

CAO Yongyan, LIN Zongli, HU Tingshu. Stability analysis of linear time-delay systems subject to input saturation [J]. IEEE Transactions on Circuits and Systems: I Fundamental Theory and Applications, 2002, 49(2): 233-240.

FRIDMAN E, ORLOV Y. Exponential stability of linear distributed parameter systems with time-varying delays [J]. Automatica, 2009, 45(1): 194-201.

KIM J H. Improved ellipsoidal bound of reachable sets for time-delayed linear systems with disturbances [J]. Automatica, 2008, 44(11): 2940-2943.

FAN Kuo-Kuang, CHEN Jenq-Der, LIEN Chang-Hua, et al. Delay-dependent stability criterion for neutral time-delay systems via linear matrix inequality approach [J]. Journal of Mathematical Analysis and Applications, 2002, 273(2): 580-589.

IVANESCU D, DION J M, DUGARD L, et al. Dynamical compensation for time-delay systems: an LMI approach [J]. International Journal of Robust and Nonlinear Control, 2000, 10(8): 611-628.

KOLMANOVSKII V B, RICHARD J P. Stability of some linear systems with delays [J]. IEEE Transactions on Automatic Control, 1999, 44(5): 984-989.

ZHANG Xiping, TSIOTRAS P, KNOSPE C. Stability analysis of LPV time-delayed systems [J]. International Journal of Control, 2002, 75(7): 538-558.

HAN Qing-Long. A discrete delay decomposition approach to stability of linear retarded and neutral systems [J]. Automatica, 2009, 45(2): 517-524.

SHAO Hanyong. Improved delay-dependent stability criteria for systems with a delay varying in a range [J]. Automatica, 2008, 44(12): 3215-3218.

HE Yong, WANG Qing-Guo, LIN Chong, et al. Delay-range-dependent stability for systems with time-varying delay [J]. Automatica, 2007, 43(2): 371-376.

HU Xiao-Bing, CHEN Wen-Hua. Model predictive control for constrained systems with uncertain state-delays [J]. International Journal of Robust and Nonlinear Control, 2004, 14(17): 1421-1432.

KWON O M, PARK J H, LEE S M. On delay-dependent robust stability of uncertain neutral systems with interval time-varying delays [J]. Applied Mathematics and Computation, 2008, 203(2): 843-853.

刘健辰, 章兢, 张红强, 等. 时滞系统稳定性分析和镇定: 一种基于Finsler引理的统一观点 [J]. 控制理论与应用, 2011, 28(11): 1577-1582.

LIU Jianchen, ZHANG Jing, ZHANG Hongqiang, et al. Stability analysis and stabilization for time-delay systems: a unified viewpoint of Finsler's lemma [J]. Control Theory Applications, 2011, 28(11): 1577-1582.

张红强, 刘健辰. 基于二次分离方法的时变时滞系统稳定性分析 [J]. 控制与决策, 2011, 26(10): 1596-1600.

ZHANG Hongqiang, LIU Jianchen. Stability analysis for time-varying delay systems based on quadratic separation approach [J]. Control and Decision, 2011, 26(10): 1596-1600.

FRIDMAN E. New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems [J]. Systems and Control Letters, 2001, 43(4): 309-319.

HE Yong, WU Min, SHE Jin-Hua, et al. Delay-range-dependent stability for systems with time-varying delay [J]. IEEE Transactions on Automatic Control, 2004, 49(5): 828-832.

HUANG Wenzhang. Generalization of Liapunov's theorem in a linear delay system [J]. Journal of Mathematical Analysis and Applications, 1989, 142(1): 83-94.

GU Keqin. A further refinement of discretized Lyapunov functional method for the time-delay systems [C]∥Proceedings of the American Control Conference. Piscataway, NJ, USA: IEEE, 2001: 3998-4003.

SHENG Jie, ELBEYLI O, SUNG Jian-Qiao. Stability and optimal feedback controls for time-delayed linear periodic systems [J]. AIAA Journal, 2004, 42(5): 908-911.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Effect of Control Delay on Dynamic Characteristics of Negative Stiffness Duffing System

A Hybrid-Topology Overlay Network for Supporting Large-Scale Application-Level Multicast

Dynamics in the Evolution of Spherical Micro-Bubble in Water and Its Control

Model for Cable-in-Conduit Conductor(CICC) Design Considering Strain Effect

Stability Analysis of Active Vibration Control System Involving Double Time Delays

Related Author

李辉光 1

刘恒 1

杨利花 1

虞烈 1

姜山 1

2 董巍 1

Related Institution

Institute of Mechatronics and Information System, Xi'an Jiaotong University

Ministry of Education Key Lab for Intelligent Networks and Network Security, Xi'an Jiaotong University

Department of Computer Science and Technology, Xi'an Jiaotong University

School of Energy and Power Engineering, Xi'an Jiaotong University

School of Information Science and Engineering, Henan University of Technology

⁰