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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.
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Keywords:
- discrete-time descriptor systems /
- switched systems /
- uniform finite-time stability /
- state feedback
[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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[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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