东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2012, Vol. 33 ›› Issue (1): 21-24+34.DOI: -

• 论著 • 上一篇    下一篇

基于增广Lyapunov泛函的时滞系统鲁棒H_∞控制

李圣涛;井元伟;刘小梅;   

  1. 东北大学信息科学与工程学院;东南大学自动化学院;
  • 收稿日期:2013-06-19 修回日期:2013-06-19 发布日期:2013-01-17
  • 通讯作者: -
  • 作者简介:-
  • 基金资助:
    国家高技术研究发展计划项目(2010AA101702)

Robust H∞ control for time-delay systems based on augmented Lyapunov functionals

Li, Sheng-Tao (1); Jing, Yuan-Wei (1); Liu, Xiao-Mei (2)   

  1. (1) School of Information Science and Engineering, Northeastern University, Shenyang 110819, China; (2) School of Automation, Southeast University, Nanjing 210096, China
  • Received:2013-06-19 Revised:2013-06-19 Published:2013-01-17
  • Contact: Li, S.-T.
  • About author:-
  • Supported by:
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摘要： 研究了一类时滞系统的鲁棒H∞控制问题.利用增广Lyapunov泛函并结合自由权矩阵方法,以严格线性矩阵不等式(LMIs)的形式给出了保证闭环系统渐近稳定且具有给定H∞性能的改进的时滞相关有界实引理(BRL).基于得到的BRL,以LMIs的可行解给出了记忆型的状态反馈H∞控制律.当时滞系统存在范数有界不确定性时,同样地给出了基于LMIs的记忆型鲁棒H∞控制律的具体设计方法.仿真实例表明了该方法的有效性以及更小保守性.

关键词: 时滞系统, H∞控制, 时滞相关, 线性矩阵不等式(LMIs), 有界实引理

Abstract: The problem of delay-dependent robust H∞ control for systems with state-delay was investigated. An improved delay-dependent bounded real lemma (BRL) was established in terms of linear matrix inequalities (LMIs) by using augmented Lyapunov functionals and free-weighting matrices method, ensuring the resultant closed-loop system asymptotically stable and a prescribed H∞ performance level. Based on the obtained BRL, the state feedback H∞ control law with memory was given in terms of the feasible solutions of LMIs. When the time-varying norm-bounded uncertainties appeared in a time-delay system, the explicit design approach of the robust H∞ controller was also given and formulated in the form of LMIs. Numerical examples are provided to demonstrate the reduced conservatism and validity of the proposed conditions.

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