切换奇异系统的有限时间稳定

张耀利; 吴保卫; 王月娥; 韩晓霞

doi:10.7498/aps.63.170205

摘要

本文研究了一类连续切换奇异系统的有限时间稳定和状态反馈控制问题. 首先，讨论了连续切换奇异系统解的存在条件，然后给出连续切换奇异系统有限时间稳定和有限时间有界的概念；其次，利用模型依赖平均驻留时间方法和Lyapunov函数方法，分别给出切换奇异系统是正则、脉冲自由且有限时间稳定和有限时间有界的充分条件，并设计状态反馈控制器，使得闭环系统有限时间稳定和有限时间有界且具有H性能指标；最后通过数值算例验证了本文方法的有效性.

关键词:

Abstract

In this paper, finite-time stability and stabilization of switched singular systems are studied. Firstly, we discuss the solvability condition of the switched singular system and introduce the concepts of finite-time stability and finite-time boundness. Secondly, using the mode-dependent average dwell time method and the Lyapunov function method, we provide sufficient conditions to guarantee that the switched singular system is regular, impulse free, and finite-time stable or finite-time bounded. Then, we design the state feedback controllers to ensure that a closed-loop system is finite-time stable and finite-time bounded with a present H disturbance attenuation level . Finally, numerical examples are given to verify the efficiency of the proposed theory.

Keywords:

作者及机构信息

1.
陕西师范大学, 数学与信息科学学院, 西安 710062

基金项目: 国家自然科学基金（批准号：11371233）资助的课题.

Authors and contacts

1.
College of mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11371233).

参考文献

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施引文献

[1]	Xu S Y, Lam J 2006 Robust Control and Filtering of Singular Systems (New York: Springer) p12
[2]
[3]	Liu L L, Peng J G, Wu B W 2011 Appl. Math. Lett. 24 703
[4]	Wang Y E, Zhao J, Jiang B 2013 IEEE Trans. Autom. Control. 58 2114
[5]
[6]	Lin H, Antsaklis P J 2009 IEEE Trans. Autom. Control. 54 308
[7]
[8]	Zhao X D, Zhang L X, Shi P, Liu M 2012 IEEE Trans. Autom. Control. 57 1809
[9]
[10]	Lin X Z, Du H B, Li S H 2011 Control and Decision 26 841 (in Chinese)[林相泽, 都海波, 李世华 2011 控制与决策 26 841]
[11]
[12]	Liu H, Zhao X D 2014 J. Franklin Inst. 351 1301
[13]
[14]
[15]	Wu L F, Guan Y, Liu Y 2013 Acta Phys. Sin. 62 110510 (in Chinese)[吴立锋, 关永, 刘勇 2013 62 110510]
[16]
[17]	Cao W, Sun M 2014 Acta Phys. Sin. 63 020201 (in Chinese)[曹伟, 孙明 2014 63 020201]
[18]	Liberzon D, Trenn S 2009 Proceedings of the 48th IEEE Conference on Decision and Control Shanghai, China, December 16-18, 2009 p2156
[19]
[20]
[21]	Raouf J, Michalska H 2010 Proceedings of the 49th IEEE Conference on Decision and Control Hilton Atlanta Hotel, Atlanta, GA, USA, December 15-17, 2010 p414
[22]
[23]	Shi S, Zhang Q, Yuan Z, Liu W 2011 IET Control Theory A. 5 103
[24]	Ma S P, Zhang C H, Wu Z 2008 Appl. Math. Comput. 206 413
[25]
[26]
[27]	Kimball J W, Krein P T 2008 IEEE Trans. Power Electron. 23 2970
[28]
[29]	Lin J X, Fei S M 2010 Acta Autom. Sin. 36 1773
[30]
[31]	Clotet J, Ferrer J, Magret M D 2009 17th Mediterranean Conference on Control and Automation Thessaloniki, Greece, June 24-26, 2009 p1343
[32]
[33]	Zhang Y Q, Liu C X, Mu X W 2012 Appl. Math. Comput. 218 5629
[34]	Gao Z R, Shen Y X 2012 Acta Phys. Sin. 61 120203
[35]
[36]	Yang K, Shen Y X, Ji C G 2013 J. Syst. Eng. Electron. 35 373 (in Chinese)[杨　坤, 沈艳霞, 纪志成 2013 系统工程与电子技术 35 373]
[37]
[38]	Gao Z R 2012 Ph. D. Dissertation (Wuxi: Jiangnan University) (in Chinese)[高在瑞 2012 博士学位论文 (无锡:江南大学)]
[39]
[40]	Ruan N N 2012 M. S. Dissertation (Nanjing: Institutes of Technology of Nanjing) (in Chinese)[阮楠楠 2012 硕士学位论文 (南京: 南京理工大学)]
[41]
[42]	Dorata P 1961 Proc. IRE Int. Conv. Rec. 4 83
[43]
[44]
[45]	Amato F, Ariola M, Dorato P 2001 Automatica 37 1459
[46]
[47]	Zhong D, Gao S G, Zhao H, Ma Y J, Liu S J 2011 Chin. Phys. B 20 120501
[48]	Li P 2013 Chin. Phys. B 22 070501
[49]
[50]
[51]	Guo S P, Li D X, Meng Y H, Fan C Z 2014 Chin. Phys. B 23 054502
[52]
[53]	Huang F, Wu B W 2012 CQUNJ 29 51 (in Chinese)[黄发, 吴保卫重庆师范大学学报 (自然科学版) 2012 29 51]

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