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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.
[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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[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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