[1] Xue Mingxiang, Fei Shumin, Li Tao, et al. New criterion for delay-dependent absolute stabilityof Lurie system with interval time-varying delay [J]. Journal of Southeast University (English Edition), 2011, 27 (4): 375-378. [doi:10.3969/j.issn.1003-7985.2011.04.006]

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New criterion for delay-dependent absolute stabilityof Lurie system with interval time-varying delay()

区间变时滞Lurie系统的绝对稳定新准则

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

27

Issue:

2011 4

Page:

375-378

Research Field:

Automation

Publishing date:

2011-12-31

Info

Title:

New criterion for delay-dependent absolute stabilityof Lurie system with interval time-varying delay

区间变时滞Lurie系统的绝对稳定新准则

Author(s):

Xue Mingxiang¹;  2;  Fei Shumin¹;  Li Tao³;  Pan Juntao¹(¹ Key Laboratory of Measurement and Control of Complex Systems of Engineering of Ministry of Education;  Southeast University;  Nanjing 210096;  China)

² School of Mathematical Sciences, Anhui University, Hefei 230601, China
³ School of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210007, China

薛明香¹;  2;  费树岷¹;  李涛³;  潘俊涛¹

¹ 东南大学复杂工程系统测量与控制教育部重点实验室, 南京 210096; ²安徽大学数学科学学院, 合肥 230601; ³ 南京航空航天大学自动化学院, 南京 210007

Keywords:

Lurie system;  reciprocal convex technique;  absolute stability;  interval time-varying delay;  linear matrix inequality(LMI)

Lurie系统;  反凸组合技术;  绝对稳定;  区间变时滞;  线性矩阵不等式(LMI)

PACS:

TP13

DOI:

10.3969/j.issn.1003-7985.2011.04.006

Abstract:

The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities(LMIs). By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.

研究了一类具有区间变时滞的Lurie系统时滞相关绝对稳定性问题.利用增广Lyapunov泛函, 结合自由权矩阵方法和反凸组合技术, 提出了一种新的基于线性矩阵不等式的稳定性条件.通过保留Lyapunov泛函导数中常被忽略的有用信息, 使得到的稳定性充分条件不仅依赖于时滞的上下界和时滞导函数的上下界, 还依赖于它们的差, 与已有文献的结果相比, 具有更广泛的应用背景.此外, 在处理非线性函数的扇形域时, 给出了非线性函数的一种新的等式描述, 和已有文献中的凸描述相比, 要验证的线性矩阵不等式较少, 因此具有更低的保守性.仿真实例表明了所提方法的有效性.

References:

[1] Han Q L. Absolute stability of time-delay systems with sector-bounded nonlinearity [J]. Automatica, 2005, 41(12): 2171-2176.
[2] Han Q L, Yue D. Absolute stability of Lur’e systems with time-varying delay [J]. IET Control Theory Appl, 2007, 1(3): 854-859.
[3] Chen Y G, Zhang Y H, Li Q B. Delay-dependent absolute stability of Lur’e systems with interval time-varying delay [C]//IEEE International Conference on Networking, Sensing and Control. Sanya, China, 2008:1696-1699.
[4] He Y, Wang Q, Lin C, et al. Delay-range-dependent stability for systems with time-varying delay[J]. Automatica, 2007, 43(2): 371-376.
[5] Shao H Y. New delay-dependent stability criteria for systems with interval delay [J]. Automatica, 2009, 45(3): 744-749.
[6] Park P G, Ko J W, Jeong C. Reciprocally convex approach to stability of systems with time-varying delays [J]. Automatica, 2011, 47(1): 235-238.
[7] Gu K. Integral inequality in the stability problem of time-varying systems[C]//Proceedings of the 39th IEEE Conference on Decision and Control. Sydney, Australia, 2000: 2805-2810.
[8] Lee S M, Park J H, Kwon O M. Improved asymptotic stability analysis for Lur’e systems with sector and slope restricted nonlinearities [J]. Physics Letters A, 2007, 362(5/6): 348-351.
[9] Yan H C, Zhang H, Meng M Q H. Delay-range-dependent robust H_∞ control for uncertain systems with interval time-varying delays [J]. Neurocomputing, 2010, 73(7/8/9): 1235-1243.
[10] Yue D, Tian E G, Wang Z D, et al. Stabilization of systems with probabilistic interval input delays and its applications to networked control systems [J]. IEEE Transactions on Systems, Man and Cybernetics, Part A, 2009, 30(4): 939-945.

Memo

Memo:

Biographies: Xue Mingxiang(1979—), female, graduate; Fei Shumin(corresponding author), male, doctor, professor, smfei@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No. 60835001, 60875035, 60905009, 61004032, 61004064, 11071001), China Postdoctoral Science Foundation(No. 201003546), the Ph.D. Programs Foundation of Ministry of Education of China(No. 20093401110001), the Major Program of Higher Education of Anhui Province(No. KJ2010ZD02), the Natural Science Research Project of Higher Education of Anhui Province(No. KJ2011A020).
Citation: Xue Mingxiang, Fei Shumin, Li Tao, et al.New criterion for delay-dependent absolute stability of Lurie system with interval time-varying delay[J].Journal of Southeast University(English Edition), 2011, 27(4):375-378.[doi:10.3969/j.issn.1003-7985.2011.04.006]

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