离散时间切换广义系统的一致有限时间稳定性

高在瑞; 沈艳霞; 纪志成

doi:10.7498/aps.61.120203

摘要

针对一类离散时间切换广义系统, 研究其一致有限时间稳定性问题. 首先, 把广义系统的有限时间稳定性概念推广到离散切换广义系统; 然后, 利用Lyapunov-like函数方法, 给出了离散切换广义系统在任意给定的切换规则下是正则、因果的, 且有限时间有界和有限时间稳定的充分条件, 同时给出了保证离散切换广义系统一致有限时间稳定的状态反馈控制器的具体设计方法. 仿真算例结果说明了该控制方法的有效性.

关键词:

Abstract

The problem of uniform finite-time stability for a class of discrete-time switched descriptor systems is considered. Firstly, the concept of finite-time stability for continuous descriptor systems is extended to discrete-time switched descriptor systems. Secondly, based on the Lyapunov-like function method, and under arbitrary switching signal, sufficient conditions under which discrete-time switched descriptor systems are regular and causal, the uniform finite-time is bounded and uniform finite-time is stable, are derived. Then, the state feedback controllers are designed to guarantee the discrete-time switched descriptor system uniform finite-time stablility. Finally, some numerical examples show that the results obtained in this paper are effective.

Keywords:

作者及机构信息

1.
轻工过程先进控制教育部重点实验室; 江南大学电气自动化研究所, 无锡 214122

基金项目: 国家自然科学基金(批准号: 61174032), 教育部新世纪优秀人才支持计划(批准号: NCET-10-0437)和中央高校基本科研业务费专项资金(批准号: JUDCF10063)资助的课题.

Authors and contacts

1.
Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education; Institute of Electrical Automation, Jiangnan University, Wuxi 214122, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61174032), the New Century Excellent Talents in University (Grant No. NCET-10-0437), and the Fundamental Research Funds for the Central Universities (Grant No. JUDCF10063).

参考文献

[1]	Ma Y C, Zhang Q L 2007 Acta Phys. Sin. 56 1958 (in Chinese) [马跃超, 张庆灵 2007 56 1958]
[2]	Zhao J L, Wang J, Wei W 2011 Acta Phys. Sin. 60 100203 (in Chinese) [赵建利, 王京, 魏伟 2011 60 100203]
[3]	Feng J E, Wu Z, Sun J B 2005 Acta Automatica Sinica 31 634
[4]	Luo S K 2004 Acta Phys. Sin. 53 5 (in Chinese) [罗绍凯 2004 53 5]
[5]	Boukas E 2009 Stochastic Analysis and Application 27 637
[6]	Liberzon D 1999 IEEE Control System Magazine 19 59
[7]	Zhang W A, Yu L 2009 Automatica 45 139
[8]	Minh V T, Awang M, Parman S 2011 International Journal of Control, Automation, and Systems 9 1220
[9]	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]
[10]	Allerhand I L, Shaked U 2011 IEEE Transactions on Automatic Control 56 381
[11]	Gao Z R, Ji Z C 2011 Control and Decision 26 925 (in Chinese) [高在瑞, 纪志成 2011 控制与决策 26 925]
[12]	Liu W, Lu Z Y 2010 Applied Mechanics and Materials 29-32 2150
[13]	Wang T C, Gao Z R 2008 Acta Automatica Sinica 34 1013 (in Chinese) [王天成, 高在瑞 2008 自动化学报 34 1013]
[14]	Koenig D, Marx B 2009 IET Control Theory Appl. 3 661
[15]	Lin J X, Fei S M 2010 Acta Automatica Sinica 36 1773
[16]	Meng B,Zhang J F 2006 Acta Automatica Sinica 32 179
[17]	Ma S P, Zhang C H, Wu Z 2008 Applied Mathematics and Computation 206 413
[18]	Dorato P 1961 Proc of the IRE Convention record, Part 4, New York, May 9, 1961, 83
[19]	Amato F, Ambrosino R, Ariola M 2011 International Journal of Robust and Nonlinear Control 21 1080
[20]	Gao T G, Chen Z Q, Chen G R, Yuan Z Z 2006 Chin. Phys. 15 1190
[21]	Wei D Q, Zhang B 2009 Chin. Phys. B 18 1399
[22]	Amato F, Cosentino C, Merola A 2010 IEEE Trans on Automatic Control 55 430
[23]	Orlov Y 2011 IEEE Transactions on Automatic Control 56 614
[24]	Shen Y J 2008 Control and Decision 23 107 (in Chinese) [沈艳军 2008 控制与决策 23 107]

施引文献

[1]	Ma Y C, Zhang Q L 2007 Acta Phys. Sin. 56 1958 (in Chinese) [马跃超, 张庆灵 2007 56 1958]
[2]	Zhao J L, Wang J, Wei W 2011 Acta Phys. Sin. 60 100203 (in Chinese) [赵建利, 王京, 魏伟 2011 60 100203]
[3]	Feng J E, Wu Z, Sun J B 2005 Acta Automatica Sinica 31 634
[4]	Luo S K 2004 Acta Phys. Sin. 53 5 (in Chinese) [罗绍凯 2004 53 5]
[5]	Boukas E 2009 Stochastic Analysis and Application 27 637
[6]	Liberzon D 1999 IEEE Control System Magazine 19 59
[7]	Zhang W A, Yu L 2009 Automatica 45 139
[8]	Minh V T, Awang M, Parman S 2011 International Journal of Control, Automation, and Systems 9 1220
[9]	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]
[10]	Allerhand I L, Shaked U 2011 IEEE Transactions on Automatic Control 56 381
[11]	Gao Z R, Ji Z C 2011 Control and Decision 26 925 (in Chinese) [高在瑞, 纪志成 2011 控制与决策 26 925]
[12]	Liu W, Lu Z Y 2010 Applied Mechanics and Materials 29-32 2150
[13]	Wang T C, Gao Z R 2008 Acta Automatica Sinica 34 1013 (in Chinese) [王天成, 高在瑞 2008 自动化学报 34 1013]
[14]	Koenig D, Marx B 2009 IET Control Theory Appl. 3 661
[15]	Lin J X, Fei S M 2010 Acta Automatica Sinica 36 1773
[16]	Meng B,Zhang J F 2006 Acta Automatica Sinica 32 179
[17]	Ma S P, Zhang C H, Wu Z 2008 Applied Mathematics and Computation 206 413
[18]	Dorato P 1961 Proc of the IRE Convention record, Part 4, New York, May 9, 1961, 83
[19]	Amato F, Ambrosino R, Ariola M 2011 International Journal of Robust and Nonlinear Control 21 1080
[20]	Gao T G, Chen Z Q, Chen G R, Yuan Z Z 2006 Chin. Phys. 15 1190
[21]	Wei D Q, Zhang B 2009 Chin. Phys. B 18 1399
[22]	Amato F, Cosentino C, Merola A 2010 IEEE Trans on Automatic Control 55 430
[23]	Orlov Y 2011 IEEE Transactions on Automatic Control 56 614
[24]	Shen Y J 2008 Control and Decision 23 107 (in Chinese) [沈艳军 2008 控制与决策 23 107]

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