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Volume 6 Issue 2
Mar.  2019

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2019  >  6(2): 471-477
Ruicheng Ma and Shuang An, "Minimum Dwell Time for Global Exponential Stability of a Class of Switched Positive Nonlinear Systems," IEEE/CAA J. Autom. Sinica, vol. 6, no. 2, pp. 471-477, Mar. 2019. doi: 10.1109/JAS.2018.7511264
Citation: Ruicheng Ma and Shuang An, "Minimum Dwell Time for Global Exponential Stability of a Class of Switched Positive Nonlinear Systems," IEEE/CAA J. Autom. Sinica, vol. 6, no. 2, pp. 471-477, Mar. 2019. doi: 10.1109/JAS.2018.7511264
shu

Minimum Dwell Time for Global Exponential Stability of a Class of Switched Positive Nonlinear Systems

doi: 10.1109/JAS.2018.7511264

  • School of Mathematics, Liaoning University, Shenyang 110036, China

Funds:

the National Natural Science Foundation of China 61673198

the Provincial Natural Science Foundation of Liaoning Province 20180550473

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    Abstract
  • This paper will investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching, whose nonlinear functions for each subsystem are constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are Metzler. A class of multiple time-varying Lyapunov functions is constructed to obtain the computable sufficient conditions on the stability of such switched nonlinear systems within the framework of minimum dwell time switching. All present conditions can be solved by linear/nonlinear programming techniques. An example is provided to demonstrate the effectiveness of the proposed result.

     

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    • References(29)
  • [1]
    D. Liberzon, Switching in Systems and Control, Boston: Birkhauser, 2003.
    [2]
    Z. Sun and S. S. Ge, Switched Linear Systems: Control and Design. London: Springer-Verlag, 2005.
    [3]
    L. Wu, R. Yang, P. Shi, and X. Su, "Stability analysis and stabilization of 2-d switched systems under arbitrary and restricted switchings, "Automatica, vol. 59, pp. 206-215, 2015. doi: 10.1016/j.automatica.2015.06.008
    [4]
    S. Yin, H. Gao, J. Qiu, and O. Kaynak, "Descriptor reduced-order sliding mode observers design for switched systems with sensor and actuator faults, "Automatica, vol. 76, pp. 282-292, 2017. doi: 10.1016/j.automatica.2016.10.025
    [5]
    J. Lian, C. Li, and B. Xia, "Sampled-data control of switched linear systems with application to an f-18 aircraft, "IEEE Transactions on Industrial Electronics, vol. 64, no. 2, pp. 1332-1340, 2017. doi: 10.1109/TIE.2016.2618872
    [6]
    Z. L. Wang, Q. Wang, and C. Y. Dong, "Asynchronous $H_\infty$ control for unmanned aerial vehicles: switched polytopic system approach, "IEEE/CAA Journal of Automatica Sinica, vol. 2, no. 2, pp. 207-216, 2015. http://www.ieee-jas.org/en/article/id/88cbd2ec-136f-4a71-b375-ee9987dba554
    [7]
    X. Zhao, P. Shi, Y. Yin, and S. K. Nguang, "New results on stability of slowly switched systems: A multiple discontinuous Lyapunov function approach, "IEEE Transactions on Automatic Control, vol. 62, no. 7, pp. 3502-3509, 2017. doi: 10.1109/TAC.2016.2614911
    [8]
    L. Zhang and H. Gao, "Asynchronously switched control of switched linear systems with average dwell time, "Automatica, vol. 46, no. 5, pp. 953-958, 2010. doi: 10.1016/j.automatica.2010.02.021
    [9]
    X. Zhao, S. Yin, H. Li, and B. Niu, "Switching stabilization for a class of slowly switched systems, "IEEE Transactions on Automatic Control, vol. 60, no. 1, pp. 221-226, 2015. doi: 10.1109/TAC.2014.2322961
    [10]
    L. Long, "Multiple Lyapunov functions-based small-gain theorems for switched interconnected nonlinear systems, "IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3943-3958, 2017. doi: 10.1109/TAC.2017.2648740
    [11]
    K. W. Zhu, J. Zhao, and G. M. Dimirovski, $H_\infty$ tracking control for switched LPV systems with an application to aero-engines, "IEEE/CAA Journal of Automatica Sinica, vol. 5, no. 3, 699-705, May 2018. doi: 10.1109/JAS.2016.7510025
    [12]
    X. Zhao, H. Liu, J. Zhang, and H. Li, "Multiple-mode observer design for a class of switched linear systems, "IEEE Transactions on Automation Science and Engineering, vol. 12, no. 1, pp. 272-280, 2015. doi: 10.1109/TASE.2013.2281466
    [13]
    R. Ma, J. Fu, and T. Chai, "Dwell-time-based observers design for unknown inputs switched linear systems without requiring strong detectability of subsystems, "IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 4215-4221, 2017. doi: 10.1109/TAC.2017.2683065
    [14]
    W. Xu, Z. G. Feng, J. W. Peng, and K. F. C. Yiu, "Optimal switching for linear quadratic problem of switched systems in discrete time, "Automatica, vol. 78, pp. 185-193, 2017. doi: 10.1016/j.automatica.2016.12.002
    [15]
    P. Colaneri, R. H. Middleton, Z. Chen, D. Caporale, and F. Blanchini, "Convexity of the cost functional in an optimal control problem for a class of positive switched systems, "Automatica, vol. 50, no. 4, pp. 1227-1234, 2014. doi: 10.1016/j.automatica.2014.02.025
    [16]
    R. Ma and J. Zhao, "Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings, "Automatica, vol. 46, no. 11, pp. 1819-1823, 2010. doi: 10.1016/j.automatica.2010.06.050
    [17]
    J. Fu, R. Ma, and T. Chai, "Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers, "Automatica, vol. 54, no. 4, pp. 360-373, 2015. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=0a5e64034fcb286c522d5bfe18cc3c3a
    [18]
    M. Hajiahmadi, B. De Schutter, and H. Hellendoorn, "Stabilization and robust $H_\infty$ control for sector-bounded switched nonlinear systems, "Automatica, vol. 50, no. 10, pp. 2726-2731, 2014. doi: 10.1016/j.automatica.2014.08.015
    [19]
    A. Y. Aleksandrov, Y. Chen, A. V. Platonov, and L. Zhang, "Stability analysis for a class of switched nonlinear systems, "Automatica, vol. 47, no. 10, pp. 2286-2291, 2011. doi: 10.1016/j.automatica.2011.08.016
    [20]
    Y. Sun and L. Wang, "On stability of a class of switched nonlinear systems, "Automatica, vol. 49, no. 1, pp. 305-307, 2013. doi: 10.1016/j.automatica.2012.10.011
    [21]
    X. Zhao, X. Liu, S. Yin, and H. Li, "Improved results on stability of continuous-time switched positive linear systems, "Automatica, vol. 50, no. 2, pp. 614-621, 2014. doi: 10.1016/j.automatica.2013.11.039
    [22]
    J. Zhang, J. Huang, and X. Zhao, "Further results on stability and stabilisation of switched positive systems, "IET Control Theory & Applications, vol. 9, no. 14, pp. 2132-2139, 2015. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=64bb8185aa843c3869081e0a18f85b63
    [23]
    X. Zhao, L. Zhang, P. Shi, and M. Liu, "Stability of switched positive linear systems with average dwell time switching, "Automatica, vol. 48, no. 6, pp. 1132-1137, 2012. doi: 10.1016/j.automatica.2012.03.008
    [24]
    Y. Sun, "Stability analysis of positive switched systems via joint linear copositive lyapunov functions, "Nonlinear Analysis: Hybrid Systems, vol. 19, pp. 146-152, 2016. doi: 10.1016/j.nahs.2015.09.001
    [25]
    X. Liu, "Stability analysis of switched positive systems: a switched linear copositive Lyapunov function method, "IEEE Transactions on Circuits and Systems Ⅱ: Express Briefs, vol. 56, no. 5, pp. 414-418, 2009. doi: 10.1109/TCSII.2009.2019326
    [26]
    C. Briat, "Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems, "Nonlinear Analysis: Hybrid Systems, vol. 24, no. Supplement C, pp. 198-226, 2017. http://www.sciencedirect.com/science/article/pii/S1751570X17300043
    [27]
    X. Liu, "Stability analysis of a class of nonlinear positive switched systems with delays, "Nonlinear Analysis: Hybrid Systems, vol. 16, pp. 1-12, 2015. doi: 10.1016/j.nahs.2014.12.002
    [28]
    J. Zhang, Z. Han, F. Zhu, and X. Zhao, "Absolute exponential stability and stabilization of switched nonlinear systems, "Systems & Control Letters, vol. 66, no. 4, pp. 51-57, 2014. http://www.sciencedirect.com/science/article/pii/S0167691114000115
    [29]
    L. Farina and S. Rinaldi, Positive Linear Systems: Theory and Applications. John Wiley & Sons, 2011.
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