Research article

Finite-time stability and applications of positive switched linear delayed impulsive systems

  • Received: 02 October 2023 Revised: 15 February 2024 Accepted: 06 March 2024 Published: 16 May 2024
  • In this paper, we study the finite-time stability and applications of positive switched linear delayed systems under synchronous impulse control, which includes two types of random switching and average dwell time switching. By constructing a type of linear time-varying co-positive Lyapunov functional, we first propose several new finite-time stability criteria. It should be emphasized that the linear term coefficient of the linear vector of the Lyapunov functional is adjusted to the difference between the weighting vector and the given vector. Then, we apply the obtained stability criteria to the linear time-varying delayed systems with impulsive effects. At last, three examples are given to demonstrate the validity of the obtained results, which includes the specific linear programming algorithm process.

    Citation: Yanchao He, Yuzhen Bai. Finite-time stability and applications of positive switched linear delayed impulsive systems[J]. Mathematical Modelling and Control, 2024, 4(2): 178-194. doi: 10.3934/mmc.2024016

    Related Papers:

  • In this paper, we study the finite-time stability and applications of positive switched linear delayed systems under synchronous impulse control, which includes two types of random switching and average dwell time switching. By constructing a type of linear time-varying co-positive Lyapunov functional, we first propose several new finite-time stability criteria. It should be emphasized that the linear term coefficient of the linear vector of the Lyapunov functional is adjusted to the difference between the weighting vector and the given vector. Then, we apply the obtained stability criteria to the linear time-varying delayed systems with impulsive effects. At last, three examples are given to demonstrate the validity of the obtained results, which includes the specific linear programming algorithm process.



    加载中


    [1] L. Farina, S. Rinaldi, Positive linear systems: theory and applications, John Wiley & Sons, Inc., New York, 2000. https://doi.org/10.1002/9781118033029
    [2] P. De Leenheer, D. Aeyels, Stabilization of positive linear systems, Syst. Control Lett., 44 (2001), 259–271. https://doi.org/10.1016/S0167-6911(01)00146-3 doi: 10.1016/S0167-6911(01)00146-3
    [3] R. Shorten, F. Wirth, D. Leith, A positive systems model of TCP-like congestion control: asymptotic results, IEEE/ACM Trans. Network, 14 (2006), 616–629. https://doi.org/10.1109/TNET.2006.876178 doi: 10.1109/TNET.2006.876178
    [4] D. Angeli, P. De Leenheer, E. D. Somgtag, Chemical networks with inflows and outflows: a positive linear differential inclusions approach, Biotechnol. Progr., 25 (2009), 632–642. https://doi.org/10.1002/btpr.162 doi: 10.1002/btpr.162
    [5] J. Lian, C. Li, B. Xia, Sampled-data control of switched linear systems with application to an F-18 aircraft, IEEE Trans. Ind. Electron., 64 (2016), 1332–1340. https://doi.org/10.1109/TIE.2016.2618872 doi: 10.1109/TIE.2016.2618872
    [6] Y. Sun, Y. Tian, X. Xie, Stabilization of positive switched linear systems and its application in consensus of multiagent systems, IEEE Trans. Autom. Control, 62 (2017), 6608–6613. https://doi.org/10.1109/TAC.2017.2713951 doi: 10.1109/TAC.2017.2713951
    [7] M. Xiang, Z. Xiang, Stability, $L_{1}$-gain and control synthesis for positive switched systems with time-varying delay, Nonlinear Anal. Hybrid Syst., 9 (2013), 9–17. https://doi.org/10.1016/j.nahs.2013.01.001 doi: 10.1016/j.nahs.2013.01.001
    [8] S. Liu, Z. Xiang, Exponential $L_{1}$ output tracking control for positive switched linear systems with time-varying delays, Nonlinear Anal. Hybrid Syst., 11 (2014), 118–128. https://doi.org/10.1016/j.nahs.2013.07.002 doi: 10.1016/j.nahs.2013.07.002
    [9] X. Liu, Stability analysis of a class of nonlinear positive switched systems with delays, Nonlinear Anal. Hybrid Syst., 16 (2015), 1–12. https://doi.org/10.1016/j.nahs.2014.12.002 doi: 10.1016/j.nahs.2014.12.002
    [10] Y. Sun, Stability analysis of positive switched systems via joint linear copositive Lyapunov functions, Nonlinear Anal. Hybrid Syst., 19 (2016), 146–152. https://doi.org/10.1016/j.nahs.2015.09.001 doi: 10.1016/j.nahs.2015.09.001
    [11] W. Zhao, Y. Sun, Absolute exponential stability of switching Lurie systems with time-varying delay via dwell time switching, J. Franklin Inst., 360 (2023), 11871–11891. https://doi.org/10.1016/j.jfranklin.2023.09.023 doi: 10.1016/j.jfranklin.2023.09.023
    [12] F. Amato, R. Ambrosino, M. Ariola, G. De Tommasi, Robust finite-time stability of impulsive dynamical linear systems subject to norm-bounded uncertainties, Int. J. Robust Nonlinear Control, 21 (2011), 1080–1092. https://doi.org/10.1002/rnc.1620 doi: 10.1002/rnc.1620
    [13] G. Garcia, S. Tarbouriech, J. Bernussou, Finite-time stabilization of linear time-varying continuous systems, IEEE Trans. Autom. Control, 54 (2009), 364–369. https://doi.org/10.1109/TAC.2008.2008325 doi: 10.1109/TAC.2008.2008325
    [14] S. Zhao, J. Sun, L. Liu, Finite-time stability of linear time-varying singular systems with impulsive effects, Int. J. Control, 81 (2008), 1824–1829. https://doi.org/10.1080/00207170801898893 doi: 10.1080/00207170801898893
    [15] K. Wang, E. Tian, S. Shen, L. Wei, J. Zhang, Input-output finite-time stability for networked control systems with memory event-triggered scheme, J. Franklin Inst., 356 (2019), 8507–8520. https://doi.org/10.1016/j.jfranklin.2019.08.020 doi: 10.1016/j.jfranklin.2019.08.020
    [16] N. T. Thanh, P. Niamsup, V. N. Phat, Finite-time stability of singular nonlinear switched time-delay systems: a singular value decomposition approach, J. Franklin Inst., 354 (2017), 3502–3518. https://doi.org/10.1016/j.jfranklin.2017.02.036 doi: 10.1016/j.jfranklin.2017.02.036
    [17] J. Wei, X. Zhang, H. Zhi, X. Zhu, New finite-time stability conditions of linear discrete switched singular systems with finite-time unstable subsystems, J. Franklin Inst., 357 (2020), 279–293. https://doi.org/10.1016/j.jfranklin.2019.03.045 doi: 10.1016/j.jfranklin.2019.03.045
    [18] T. Zhang, F. Deng, W. Zhang, Finite-time stability and stabilization of linear discrete time-varying stochastic systems, J. Franklin Inst., 356 (2019), 1247–1267. https://doi.org/10.1016/j.jfranklin.2018.10.026 doi: 10.1016/j.jfranklin.2018.10.026
    [19] L. Hou, C. Sun, H. Ren, Y. Wei, Finite-time stability of switched linear systems, Proceedings of the 36th Chinese Control Conference, 2017, 2338–2342. https://doi.org/10.23919/ChiCC.2017.8027707
    [20] W. Xiang, J. Xiao, Finite-time stability and stabilisation for switched linear systems, Int. J. Syst. Sci., 44 (2013), 384–400. https://doi.org/10.1080/00207721.2011.604738 doi: 10.1080/00207721.2011.604738
    [21] L. Liu, N. Xu, G. Zong, X. Zhao, New results on finite-time stability and stabilization of switched positive linear time-delay systems, IEEE Access, 8 (2020), 4418–4427. https://doi.org/10.1109/ACCESS.2019.2961683 doi: 10.1109/ACCESS.2019.2961683
    [22] G. Chen, Y. Yang, Finite-time stability of switched positive linear systems, Int. J. Robust Nonlinear Control, 24 (2012), 179–190. https://doi.org/10.1002/rnc.2870 doi: 10.1002/rnc.2870
    [23] N. Xu, Y. Chen, A. Xue, G. Zong, Finite-time stabilization of continuous-time switched positive delayed systems, J. Franklin Inst., 359 (2022), 255–271. https://doi.org/10.1016/j.jfranklin.2021.04.022 doi: 10.1016/j.jfranklin.2021.04.022
    [24] M. Zhang, Q. Zhu, Finite-time input-to-state stability of switched stochastic time-varying nonlinear systems with time delays, Chaos Solitons Fract., 162 (2022), 112391. https://doi.org/10.1016/j.chaos.2022.112391 doi: 10.1016/j.chaos.2022.112391
    [25] T. Huang, Y. Sun, D. Tian, Finite-time stability of positive switched time-delay systems based on linear time-varying copositive Lyapunov functional, J. Franklin Inst., 359 (2022), 2244–2258. https://doi.org/10.1016/j.jfranklin.2022.01.029 doi: 10.1016/j.jfranklin.2022.01.029
    [26] M. Hu, Y. Wang, J. Xiao, W. Yang, $L_{1}$-gain analysis and control of impulsive positive systems with interval uncertainty and time delay, J. Franklin Inst., 356 (2019), 9180–9205. https://doi.org/10.1016/j.jfranklin.2019.08.010 doi: 10.1016/j.jfranklin.2019.08.010
    [27] T. Liu, B. Wu, L. Liu, Y. Wang, Asynchronously finite-time control of discrete impulsive switched positive time-delay systems, J. Franklin Inst., 352 (2015), 4503–4514. https://doi.org/10.1016/j.jfranklin.2015.06.015 doi: 10.1016/j.jfranklin.2015.06.015
    [28] S. Peng, L. Yang, Global exponential stability of impulsive functional differential equations via Razumikhin technique, Abstr. Appl. Anal., 2010 (2010), 987372. https://doi.org/10.1155/2010/987372 doi: 10.1155/2010/987372
    [29] M. Hu, Y. Wang, J. Xiao, On finite-time stability and stabilization of positive systems with impulses, Nonlinear Anal. Hybrid Syst., 31 (2019), 275–291. https://doi.org/10.1016/j.nahs.2018.10.004 doi: 10.1016/j.nahs.2018.10.004
    [30] M. Hu, J. Xiao, R. Xiao, W. Chen, Impulsive effects on the stability and stabilization of positive systems with delays, J. Franklin Inst., 354 (2017), 4034–4054. https://doi.org/10.1016/j.jfranklin.2017.03.019 doi: 10.1016/j.jfranklin.2017.03.019
    [31] C. Briat, Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems, Nonlinear Anal. Hybrid Syst., 24 (2017), 198–226. https://doi.org/10.1016/j.nahs.2017.01.004 doi: 10.1016/j.nahs.2017.01.004
    [32] G. Chen, C. Fan, J. Sun, J. Xia, Mean square exponential stability analysis for itô stochastic systems with aperiodic sampling and multiple time-delays, IEEE Trans. Autom. Control, 67 (2022), 2473–2480. https://doi.org/10.1109/TAC.2021.3074848 doi: 10.1109/TAC.2021.3074848
    [33] G. Chen, J. Xia, Ju H. Park, H. Shen, G. Zhuang, Sampled-data synchronization of stochastic Markovian jump neural networks with time-varying delay, IEEE Trans. Neural Networks Learn. Syst., 33 (2021), 3829–3841. https://doi.org/10.1109/TNNLS.2021.3054615 doi: 10.1109/TNNLS.2021.3054615
    [34] G. Chen, G. Du, J. Xia, X. Xie, J. H. Park, Controller synthesis of aperiodic sampled-data networked control system with application to interleaved flyback module integrated converter, IEEE Trans. Circuits Syst. I, 70 (2023), 4570–4580. https://doi.org/10.1109/TCSI.2023.3295940 doi: 10.1109/TCSI.2023.3295940
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(675) PDF downloads(106) Cited by(0)

Article outline

Figures and Tables

Figures(11)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog