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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 (2): 239-250.doi: 10.3969/j.issn.1005-3085.2015.02.008

• • 上一篇    下一篇

含非线性扰动的混合变时滞中立系统鲁棒稳定性新判据

吴玉彬1,   张合新1,   惠俊军1,2,   周   鑫1   

  1. 1- 第二炮兵工程大学自动控制系，西安 710025
    2- 陕西省宝鸡市150信箱11分箱，宝鸡 721013
  • 收稿日期:2013-07-17 接受日期:2014-01-17 出版日期:2015-04-15 发布日期:2015-06-15
  • 基金资助:
    国家自然科学基金 (61374120).

New Robust Stability Criteria for Neutral Systems with Mixed Time-varying Delays and Nonlinear Perturbation

WU Yu-bin1,   ZHANG He-xin1,   HUI Jun-jun1,2,   ZHOU Xin1   

  1. 1- Department of Automation, The Second Artillery Engineering University, Xi'an 710025
    2- Mailbox 150 Extension 11, Baoji 721013
  • Received:2013-07-17 Accepted:2014-01-17 Online:2015-04-15 Published:2015-06-15
  • Supported by:
    The National Natural Science Foundation of China (61374120).

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摘要： 中立型时滞系统在工程实际中有着广泛应用背景．本文研究了一类含非线性扰动的混合变时滞中立型系统地鲁棒稳定性问题．基于直接Lyapunov泛函方法，通过构造一类新的包含时滞区间上下界的三重积分项Lyapunov-Krasovskii泛函，并结合积分不等式方法、自由权矩阵技术和凸组合处理方法，建立了一种新的线性矩阵不等式形式的离散时滞和中立时滞均相关的鲁棒稳定性判据．最后，通过数值算例验证了新判据的有效性和优越性，和一些已有文献相比，本文提出的判据具有更低的保守性．

关键词: 中立系统, Lyapunov-Krasovskii泛函, 鲁棒稳定, 非线性扰动, 线性矩阵不等式

Abstract:

Neutral time delay system is a special system which has wide application in prac-tical systems. In this paper, we consider the delay-dependent robust stability problem for neutral system with mixed time-varying delays and nonlinear perturbation. Based on the direct Lyapunov method, a new Lyapunov-Krasovskii (L-K) functional with triple integral terms involving lower and upper bounds of interval time-varying delays is constructed for the system. Then, combined with the integral inequalities method, the free weighting matrix approach and the convex combination technique, a neutral and discrete delay-dependent stability criteria for the system is formulated in terms of linear matrix inequalities (LMIs). Finally, the numerical examples are presented to illustrate the effectiveness and improvement over some existing results in the literature with the proposed results.

Key words: neutral system, Lyapunov-Krasovskii (L-K) functional, robust stability, nonlinear perturbations, linear matrix inequality (LMI)

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