依赖延迟线性时滞系统的稳定性判据

朱莹; 高其娜; 肖扬

doi:10.3724/SP.J.1004.2013.02150

依赖延迟线性时滞系统的稳定性判据

doi: 10.3724/SP.J.1004.2013.02150

朱莹^1,2,
高其娜^1,2,
肖扬³

1.
北京航空航天大学电子与信息工程学院北京 100191;
2.
北京航空技术研究中心北京 100076;
3.
北京交通大学计算机与信息技术学院北京 100044

基金项目:

国家自然科学基金（60572093）资助，国防科研课题（102476）资助

详细信息

作者简介:
朱莹北京航空航天大学电子与信息工程学院博士研究生. 北京航空技术研究中心高级工程师. 主要研究方向为多维系统设计和通信与电子系统. 本文通信作者. E-mail：zhuying713272@126.com

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出版历程
- 收稿日期: 2012-04-01
- 修回日期: 2012-09-19
- 刊出日期: 2013-12-20

Stability Criteria of Linear Time-delay Systems with Dependent Delays

1.
School of Electronic and Information Engineering, Beihang University, Beijing 100191;
2.
Beijing Aeronautical Technology Research Center, Beijing 100076;
3.
School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044

Funds:

Supported by National Natural Science Foundation of China (60572093) and National Defence Project (102476)

摘要

摘要: 由于独立延迟线性时滞（Linear time-delay with independent delays，LTD-ID）系统的稳定条件对系统参数有严格的限制，只有极少数依赖延迟线性时滞（LTD with dependent delays，LTD-DD）系统可满足该稳定条件. LTD-ID 系统的特征多项式属拟多项式，其根为多重延迟的函数，这使得LTD-ID系统的稳定性检验非常困难. 为解决该问题，基于二维域混合多项式，本文提出LTD-DD系统的若干稳定性判据. 应用例表明所提出的稳定性判据是简单的和有效的，所提出的定理4可解决现有LMI稳定性判据的保守性问题.
- 控制理论 /
- 时滞系统 /
- 拟多项式 /
- 二维多项式 /
- 稳定性判据
Abstract: This paper reveals that only fewer of the linear time-delay (LTD) systems with dependent delays (LTD-DD systems) can satisfy the stability condition for linear time-delay systems with independent delays (LTD-ID systems), since there is a strict limitation for the parameters of the LTD-DD systems. The characteristic polynomials of LTD-DD systems belong to quasipolynomials, and the roots of the quasipolynomials are the function of the multiple delays, which make the stability test of LTD-DD systems difficult. To solve the problem, based on 2-D hybrid polynomials, some stability criteria of LTD-DD systems are proposed. Examples show that the proposed stability criteria are simple and valid, and that the proposed theorem can solve the conservatism problem of existing LMI stability testing algorithms.
- Control theory /
- time-delay systems /
- quasipolynomials /
- two-dimensional polynomials /
- stability criteria

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参考文献(13)

[1]	Fridman E, Shaked U. An improved stabilization method for linear time-delay systems. IEEE Transactions on Automatic Control, 2002, 47(11): 1931-1937
[2]	Xu S Y, Lam J, Zou Y. Further results on delay-dependent robust stability conditions of uncertain neutral systems. International Journal of Robust and Nonlinear Control, 2005, 15(5): 233-246
[3]	Zhang Xian-Ming, Wu Min, He Yong. Delay-dependent stability for linear neutral type systems with delay. Acta Automatica Sinica, 2004, 30(3): 624-628(张先明, 吴敏, 何勇. 中立型线性时滞系统的时滞相关稳定性. 自动化学报, 2004, 30(4): 624-628)
[4]	Li T, Gao L, Lin C. A new criterion of delay-dependent stability for uncertain time-delay systems. IET Control Theory and Applications, 2007, 1(3): 611-616
[5]	Park G S, Choi H L, Lim J T. On stability of linear time-delay systems with multiple delays. International Journal of Systems Science, 2008, 39(8): 839-852
[6]	Du B, Lam J, Shu Z, Wang Z. A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components. IET Control Theory and Applications, 2009, 3(4): 383-390
[7]	Xiao Y. 2-D algebraic test for robust stability of time-delay systems with interval parameters. Journal of Systems Engineering and Electronics, 2006, 17(4): 802-810
[8]	Xiao Y. 2-D algebraic test for robust stability of quasipolynomials with interval parameters. Asian Journal of Control, 2006, 8(2): 174-179
[9]	Xiao Yang, Kim K. Stability test for time-delay partial differential equation systems. Journal of Applied Sciences Electronics and Information Engineering, 2008, 26(6): 655-660 (肖扬, Kim K. 时滞偏微分方程系统的稳定性检验. 应用科学学报, 2008, 26(6): 655-660)
[10]	Xiao Yang. Stability Analysis of Multidimensional Systems. Shanghai: Shanghai Scientific and Technical Publishers, 2003. 187-191(肖扬. 多维系统的稳定性分析. 上海: 上海科学技术出版社, 2003. 187-191)
[11]	Chen J, Niculescu S I, Fu P L. Robust stability of quasi-polynomials: frequency-sweeping conditions and vertex tests. IEEE Transactions on Automatic Control, 2008, 53(5): 1219-1234
[12]	Munz U, Ebenbauer C T, Haag T, Allgower F. Stability analysis of time-delay systems with incommensurate delays using positive polynomials. IEEE Transactions on Automatic Control, 2009, 54(5): 1019-1024
[13]	Sipahi R, Delice I I. Advanced clustering with frequency sweeping methodology for the stability analysis of multiple time-delay systems. IEEE Transactions on Automatic Control, 2011, 56(2): 467-472