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This paper addresses the stabilization problem of a class of switched linear systems. Due to the presence of switching delay in the switching signal of the controller, the switching of the controller and the of the system are turned out to be asynchronous. By combining switching signal method with the multiple Lyapunov function method, some sufficient conditions are provided to guarantee the stability of the whole switched system by an adjacent mode-dependent average dwell time scheme. These conditions imply the relationship among the continuous dynamics, switching delay, and the average dwell time. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.
[1] Liberzon D, Morse A S 1999 IEEE Contr. Syst. Mag. 19 59
[2] Cheng D Z, Guo Y Q 2005 Control Theory & Applications 22 954 (in Chinese) [程代展, 郭宇骞 2005 控制理论与应用 22 954]
[3] Zhao J, Hill D J 2008 Automatica 44 1220
[4] Sun X M, Wang W 2012 Automatica 48 2359
[5] Wang D, Wang W, Shi P 2009 IEEE Trans. Syst., Man, Cybern. B, Cybern. 39 800
[6] Wang D, Shi P, Wang W 2010 IET Control Theory Appl. 4 100
[7] Lian J, Shi P, Feng Z 2013 IEEE Trans. Cybern. 4 3
[8] Niu B, Zhao J 2013 Int. J. Syst. Sci. 44 978
[9] Zhang J L, Zhang H G, Luo Y H, Feng T 2014 Neurocomputing 133 163
[10] Cao W, Guo Y, Sun M 2014 Acta Phys. Sin. 63 180202 (in Chinese) [曹伟, 郭媛, 孙明 2014 物理学报 63 180202]
[11] Zhang Y L, Wu B W, Wang Y E, Han X X 2014 Acta Phys. Sin. 63 170205 (in Chinese) [张耀利, 吴保卫, 王月娥, 韩晓霞 2014 物理学报 63 170205]
[12] Duan G R, Wang H Q 2005 Acta Aeronaut. Astronaut. Sin. 26 144 (in Chinese) [段广仁, 王好谦 2005 航空学报 26 144]
[13] 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]
[14] Wu Z H, Peng L, Xie L B, Wen J W 2013 Chin. Phys. B 22 128901
[15] Li L, Fang H J 2013 Chin. Phys. B 22 110505
[16] Sun F L, Zhu W 2013 Chin. Phys. B 22 110204
[17] Wang Y E, Sun X M, Shi P, Zhao J 2013 IEEE Trans. Cybern. 43 2261
[18] Wang Y E, Zhao J, Jiang B 2013 IEEE Trans. Autom. Control 58 2114
[19] Zhang L X, Gao H J 2010 Automatica 46 953
[20] Xiang Z R, Wang R H 2009 IET Control Theory and Applications 3 1041
[21] Zhang Y R 2006 Ph. D. Dissertation (Chengdu: Southwest Jiaotong University) (in Chinese) [张艳荣 2006 博士学位论文 (成都：西南交通大学)]
[22] Vu L, Kristi M A 2010 IEEE Trans. Autom. Control 55 2385
[23] Zhao X D, Zhang L X, Shi P, Liu M 2012 IEEE Trans. Autom. Control 57 1809
[24] Xiang M, Xiang Z R, Karimi H R 2014 Inform. Sciences 278 703
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[1] Liberzon D, Morse A S 1999 IEEE Contr. Syst. Mag. 19 59
[2] Cheng D Z, Guo Y Q 2005 Control Theory & Applications 22 954 (in Chinese) [程代展, 郭宇骞 2005 控制理论与应用 22 954]
[3] Zhao J, Hill D J 2008 Automatica 44 1220
[4] Sun X M, Wang W 2012 Automatica 48 2359
[5] Wang D, Wang W, Shi P 2009 IEEE Trans. Syst., Man, Cybern. B, Cybern. 39 800
[6] Wang D, Shi P, Wang W 2010 IET Control Theory Appl. 4 100
[7] Lian J, Shi P, Feng Z 2013 IEEE Trans. Cybern. 4 3
[8] Niu B, Zhao J 2013 Int. J. Syst. Sci. 44 978
[9] Zhang J L, Zhang H G, Luo Y H, Feng T 2014 Neurocomputing 133 163
[10] Cao W, Guo Y, Sun M 2014 Acta Phys. Sin. 63 180202 (in Chinese) [曹伟, 郭媛, 孙明 2014 物理学报 63 180202]
[11] Zhang Y L, Wu B W, Wang Y E, Han X X 2014 Acta Phys. Sin. 63 170205 (in Chinese) [张耀利, 吴保卫, 王月娥, 韩晓霞 2014 物理学报 63 170205]
[12] Duan G R, Wang H Q 2005 Acta Aeronaut. Astronaut. Sin. 26 144 (in Chinese) [段广仁, 王好谦 2005 航空学报 26 144]
[13] 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]
[14] Wu Z H, Peng L, Xie L B, Wen J W 2013 Chin. Phys. B 22 128901
[15] Li L, Fang H J 2013 Chin. Phys. B 22 110505
[16] Sun F L, Zhu W 2013 Chin. Phys. B 22 110204
[17] Wang Y E, Sun X M, Shi P, Zhao J 2013 IEEE Trans. Cybern. 43 2261
[18] Wang Y E, Zhao J, Jiang B 2013 IEEE Trans. Autom. Control 58 2114
[19] Zhang L X, Gao H J 2010 Automatica 46 953
[20] Xiang Z R, Wang R H 2009 IET Control Theory and Applications 3 1041
[21] Zhang Y R 2006 Ph. D. Dissertation (Chengdu: Southwest Jiaotong University) (in Chinese) [张艳荣 2006 博士学位论文 (成都：西南交通大学)]
[22] Vu L, Kristi M A 2010 IEEE Trans. Autom. Control 55 2385
[23] Zhao X D, Zhang L X, Shi P, Liu M 2012 IEEE Trans. Autom. Control 57 1809
[24] Xiang M, Xiang Z R, Karimi H R 2014 Inform. Sciences 278 703
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