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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (11): 60-64.doi: 10.6040/j.issn.1671-9352.0.2017.110

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多输入多输出线性系统的时滞界问题

鞠培军1,2,王伟1*   

  1. 1. 山东大学控制科学与工程学院, 山东 济南 250061;2. 泰山学院数学与统计学院, 山东 泰安 271021
  • 收稿日期:2017-03-18 出版日期:2017-11-20 发布日期:2017-11-17
  • 通讯作者: 王伟(1980— ),男,博士,副教授,研究方向为多智能体系统、网络控制系统、分布式滤波与控制. E-mail: w.wang@sdu.edu.cn E-mail:jpj615@163.com
  • 作者简介:鞠培军(1975— ),男,博士研究生,研究方向为时滞系统. E-mail:jpj615@163.com
  • 基金资助:
    国家自然科学基金资助项目(61573220,61573221,61633014);山东省泰山学者建设工程项目

Delay margin of linear multi-input multi-output system

JU Pei-jun1,2, WANG Wei1*   

  1. 1. School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China;
    2. School of Mathematics and Statistics, Taishan University, Taian 271021, Shandong, China
  • Received:2017-03-18 Online:2017-11-20 Published:2017-11-17

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摘要： 针对多输入多输出线性系统,已有的工作仅考虑单个不稳定极点的时滞界问题。针对两个不稳定极点的情形,给出时滞界的一些上界。通过设计适当的双线性变换,利用频域方法分别对系统含有两个不稳定实极点和一对共轭虚极点的两种情况,得到了系统时滞界的估计结果。所得结果将一些已知结果作为特例,还涵盖了更广泛的范围。算例结果验证了该方法的有效性。

关键词: 多输入多输出系统, 频域方法, 时滞界

Abstract: Previous research works of linear multi-input and multi-output system were based on one unstable pole. We study the system with two unstable poles and give some upper bounds of the delay margin. By constructing some suitable bilinear transforms and using the frequency domain method, we obtain some estimations of the delay margin of systems for the two cases with two unstable real poles and a pair of unstable conjugate complex poles. Our results are of considerable generality, including the known results as particular cases. The results of calculated example show the effectiveness of the proposed method.

Key words: multi-input multi-output system, frequency domain method, delay margin

中图分类号: 

  • TP13
[1] GU K, KHARITONOV V L, CHEN J. Stability of time-delay systems[M]. Boston: Birkhäuser, 2003.
[2] MICHIELS W, NICULESCU S-I. Stability, control and computation of time delay systems: an eigenvalue based approach[M]. 2nd ed. Philadelphia: SIAM Publications, 2014.
[3] SMITH O J M. Closer control of loops with dead time[J]. Chemical Engineering Progress, 1957, 53(5):217-219.
[4] MANITIUS A Z, OLBROT A W. Finite spectrum assignment problem for systems with delays[J]. IEEE Transactions on Automatic Control, 1979, AC-24(4):541-553.
[5] KWON W H, PEARSON A E. Feedback stabilization of linear systems with delayed control[J]. IEEE Transactions on Automatic Control, 1980, AC-25(2):266-269.
[6] ARTSTEIN Z. Linear systems with delayed controls: a reduction[J]. IEEE Transactions on Automatic Control, 1982, 27(4):869-879.
[7] KRSTIC M. Delay compensation for nonlinear, adaptive, and PDE systems[M]. Boston: Birkhäuser, 2009.
[8] DAVISON D E, MILLER D E. Determining the least upper bound on the achievable delay margin, in open problems in mathematical systems and control theory[M]. Princeton, NJ: Princeton University Press, 2004.
[9] MICHIELS W, ENGELBORGHS K, VANSEVENANT P, et al. Continuous pole placement for delay equations[J]. Automatica, 2002, 38(5):747-761.
[10] SILVA G J, DATTA A, BHATTACHARYYA S P. New results on the synthesis of PID controllers[J]. IEEE Transactions on Automatic Control, 2002, 47(2):241-252.
[11] MIDDLETON R H, MILLER D E. On the achievable delay margin using LTI control for unstable plants[J]. IEEE Transactions on Automatic Control, 2007, 52(7):1194-1207.
[12] JU P, ZHANG H. Further results on the achievable delay margin using LTI control[J]. IEEE Transactions on Automatic Control, 2016, 61(10):3134-3139.
[13] QI T, ZHU J, CHEN J. On delay radii and bounds of MIMO systems[J]. Automatica, 2017, 77:214-218.
[14] CHEN J. Logarithmic integrals, interpolation bounds, and performance limitations in MIMO feedback systems[J]. IEEE Transactions on Automatic Control, 2000, 45(6):1098-1115.
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