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Uniform finite-time stability of discrete-time switched descriptor systems

Gao Zai-Rui Shen Yan-Xia Ji Zhi-Cheng

Uniform finite-time stability of discrete-time switched descriptor systems

Gao Zai-Rui, Shen Yan-Xia, Ji Zhi-Cheng
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  • 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.
    • 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).
    [1]

    Ma Y C, Zhang Q L 2007 Acta Phys. Sin. 56 1958 (in Chinese) [马跃超, 张庆灵 2007 物理学报 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 物理学报 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 物理学报 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]

  • [1]

    Ma Y C, Zhang Q L 2007 Acta Phys. Sin. 56 1958 (in Chinese) [马跃超, 张庆灵 2007 物理学报 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 物理学报 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 物理学报 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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  • Received Date:  12 October 2011
  • Accepted Date:  08 November 2011
  • Published Online:  20 June 2012

Uniform finite-time stability of discrete-time switched descriptor systems

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

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.

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