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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (3): 317-327.doi: 10.3969/j.issn.1005-3085.2015.03.001

• •    下一篇

具有非线性扰动的线性多时变时滞系统的有记忆状态反馈控制

李伯忍   

  1. 东莞理工学院计算机学院，东莞 523808
  • 收稿日期:2013-08-29 接受日期:2014-07-28 出版日期:2015-06-15 发布日期:2015-08-15
  • 基金资助:
    国家自然科学基金 (11371154; 11071087)；东莞市科技计划项目 (2012108102005).

Memory State Feedback Control for Multiple Time-varying Delays System with Nonlinear Perturbation

LI Bo-ren   

  1. College of Computer, Dongguan University of Technology, Dongguan 523808
  • Received:2013-08-29 Accepted:2014-07-28 Online:2015-06-15 Published:2015-08-15
  • Supported by:
    The National Natural Science Foundation of  China (11371154; 11071087); the Dongguan Science and Technology Plan Project (2012108102005).

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摘要： 本文探讨一类非线性扰动满足范数有界的线性多时变时滞系统的有记忆状态反馈控制，通过构造恰当的Lyapunov泛涵，利用Jensen不等式来处理泛涵导数中的交叉项，应用线性矩阵不等式技术和Schur补引理，我们得到了系统镇定的时滞相关的充分条件，并给出了有记忆状态反馈控制器的设计方法．最后，数值例子验证了文中所得的结论的保守性更低及求解方法的有效性．

关键词: 反馈控制, Jensen不等式, 线性矩阵不等式, 时变时滞, 非线性扰动

Abstract:

This paper is concerned with the robust stabilization of multiple time-varying delays system with norm bounded nonlinear perturbations. By constructing an appropriate Lyapunov functional, dealing with the cross terms in the functional derivative by using the Jensen inequality, and utilizing the linear matrix inequality technique and Schur complement lemma, we obtain the system stabilization delay-dependent sufficient condition and a memory state feedback controller design method. Finally, a numerical example is proposed, which shows the stabilization condition is less conservative and the effectiveness of the memory state feedback controller.

Key words: feedback control, Jensen inequality, linear matrix inequality, time-varying delay, nonlinear perturbation

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