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Asynchronous stabilization of switched systems: Adjacent mode-dependent average dwell time

Wang Yue-E Wu Bao-Wei Wang Rui

Asynchronous stabilization of switched systems: Adjacent mode-dependent average dwell time

Wang Yue-E, Wu Bao-Wei, Wang Rui
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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.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61403241, 61374072, 11371233), and the China Postdoctoral Science Foundation (Grant No. 2014M560748), and the Fundamental Research Funds for the Central Universities (Grant No. GK201503011).
    [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

  • [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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    [2] Li Qing-Du, Guo Jian-Li. Algorithm for calculating the Lyapunov exponents of switching system and its application. Acta Physica Sinica, 2014, 63(10): 100501. doi: 10.7498/aps.63.100501
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    [4] Chen Zhang-Yao, Xue Zeng-Hong, Zhang Chun, Ji Ying, Bi Qin-Sheng. Oscillation behaviors and mechanism of Rayleigh oscillator with periodic switches. Acta Physica Sinica, 2014, 63(1): 010504. doi: 10.7498/aps.63.010504
    [5] Zhang Yao-Li, Wu Bao-Wei, Wang Yue-E, Han Xiao-Xia. Finite-time stability for switched singular systems. Acta Physica Sinica, 2014, 63(17): 170205. doi: 10.7498/aps.63.170205
    [6] Cao Wei, Sun Ming. Iterative learning control for discrete time-varying switched systems. Acta Physica Sinica, 2014, 63(2): 020201. doi: 10.7498/aps.63.020201
    [7] Yang Xiao-Long, Tan Xue-Zhi, Guan Kai. Spectrum handoff model based on preemptive queuing theory in cognitive radio networks. Acta Physica Sinica, 2015, 64(10): 108403. doi: 10.7498/aps.64.108403
    [8] Lin Chang-Sheng, Xiong Xing, Shi Lei, Liu Yang-Zheng, Jiang Chang-Sheng. A class of switchable 3D chaotic systems. Acta Physica Sinica, 2007, 56(6): 3107-3112. doi: 10.7498/aps.56.3107
    [9] Lin Chang-Sheng, Sun Han, Liu Yang-Zheng, Jiang Chang-Sheng. Four-dimensional switchable hyperchaotic system. Acta Physica Sinica, 2007, 56(9): 5131-5135. doi: 10.7498/aps.56.5131
    [10] Liu Yang-Zheng, Lin Chang-Sheng, Li Xin-Chao. Family of switched unified chaotic system. Acta Physica Sinica, 2011, 60(4): 040505. doi: 10.7498/aps.60.040505
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  • Received Date:  10 September 2014
  • Accepted Date:  10 October 2014
  • Published Online:  05 March 2015

Asynchronous stabilization of switched systems: Adjacent mode-dependent average dwell time

  • 1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China;
  • 2. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 61403241, 61374072, 11371233), and the China Postdoctoral Science Foundation (Grant No. 2014M560748), and the Fundamental Research Funds for the Central Universities (Grant No. GK201503011).

Abstract: 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.

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