Stabilization of switched linear systems under asynchronous switching subject to admissible edge-dependent average dwell time

Linlin HOU; Xuan MA; Haibin SUN

doi:10.1631/FITEE.2000698

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Stabilization of switched linear systems under asynchronous switching subject to admissible edge-dependent average dwell time

Regular Papers | Updated：2022-05-23

- Stabilization of switched linear systems under asynchronous switching subject to admissible edge-dependent average dwell time
- 基于异步切换和可容许边依赖平均驻留时间方法的切换线性系统镇定研究
- Frontiers of Information Technology & Electronic Engineering Vol. 23, Issue 5, Pages: 810-822(2022)
- Affiliations：
  
  1.School of Computer Science, Qufu Normal University, Rizhao276826, China
  2.College of Engineering, Qufu Normal University, Rizhao276826, China
- Author bio：
  
  ‡Corresponding author
  E-mail: maxuan24@163.com;
  E-mail: fengyun198212@163.com
- Funds：
- DOI：10.1631/FITEE.2000698
  CLC： TP13
- Accepted：07 March 2021，
  
  Published Online：11 April 2022，
  
  Published：0 May 2022
- Accepted：
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Linlin HOU, Xuan MA, Haibin SUN. Stabilization of switched linear systems under asynchronous switching subject to admissible edge-dependent average dwell time[J]. Frontiers of Information Technology & Electronic Engineering, 2022, 23(5): 810-822.
DOI：

Linlin HOU, Xuan MA, Haibin SUN. Stabilization of switched linear systems under asynchronous switching subject to admissible edge-dependent average dwell time[J]. Frontiers of Information Technology & Electronic Engineering, 2022, 23(5): 810-822. DOI： 10.1631/FITEE.2000698.

摘要

本文研究异步切换条件下切换线性系统的镇定问题。采用可容许边依赖平均驻留时间方法，设计包含慢可容许边依赖平均驻留时间和快可容许边依赖平均驻留时间的切换信号。这种切换信号设计方法消除了异步切换最大延迟事先已知的限制。构造的李雅普诺夫函数与系统模态和控制器模态均相关。给出了获取控制器增益和设计切换信号的稳定性准则及相应算法。最后，通过两个算例验证了所提结果的有效性。

Abstract

The problem of stabilizing switched linear systems under asynchronous switching is addressed. The admissible edge-dependent average dwell time method is applied to design a switching signal that comprises slow admissible edge-dependent average dwell time and fast admissible edge-dependent average dwell time. Under this switching signal

the restriction that the maximum delay of asynchronous switching is known in advance is removed. The constructed Lyapunov function is associated with both the system mode and controller mode. The stabilization criteria and the corresponding algorithm are presented to obtain the controller gains and to design the switching signal. Finally

two examples are given to demonstrate the effectiveness of the proposed results.

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references

Chang Y , Zhang S , Alotaibi ND , et al. , 2020 . Observer-based adaptive finite-time tracking control for a class of switched nonlinear systems with unmodeled dynamics . IEEE Access , 8 : 204782 - 204790 . doi: 10.1109/ACCESS.2020.3023726 http://doi.org/10.1109/ACCESS.2020.3023726

Deaecto GS , Geromel JC , Daafouz J , 2011 . Dynamic output feedback H inf control of switched linear systems . Automatica , 47 ( 8 ): 1713 - 1720 . doi: 10.1016/j.automatica.2011.02.046 http://doi.org/10.1016/j.automatica.2011.02.046

Deaecto GS , Souza M , Gernmel JC , 2015 . Discrete-time switched linear systems state feedback design with application to networked control . IEEE Trans Automat Contr , 60 ( 3 ): 877 - 881 . doi: 10.1109/TAC.2014.2341131 http://doi.org/10.1109/TAC.2014.2341131

Fei ZY , Shi S , Zhao C , et al. , 2017 . Asynchronous control for 2-D switched systems with mode-dependent average dwell time . Automatica , 79 : 198 - 206 . doi: 10.1016/j.automatica.2017.01.026 http://doi.org/10.1016/j.automatica.2017.01.026

Fei ZY , Guan CX , Zhao XD , 2020 . Event-triggered dynamic output feedback control for switched systems with frequent asynchronism . IEEE Trans Automat Contr , 65 ( 7 ): 3120 - 3127 . doi: 10.1109/TAC.2019.2945279 http://doi.org/10.1109/TAC.2019.2945279

Hespanha JP , Morse AS , 1999 . Stability of switched systems with average dwell-time . Proc 38 th IEEE Conf on Decision Control , p. 2655 - 2660 . doi: 10.1109/CDC.1999.831330 http://doi.org/10.1109/CDC.1999.831330

Hou LL , Zhao XD , Sun HB , et al. , 2018a . <math id="M441"><mrow><msub><mi>l</mi><mn>2</mn></msub><mo>−</mo><msub><mi>l</mi><mi>∞</mi></msub></mrow></math> filtering of discrete-time switched systems via admissible edge-dependent switching signals . Syst Contr Lett , 113 : 17 - 26 . doi: 10.1016/j.sysconle.2017.10.005 http://doi.org/10.1016/j.sysconle.2017.10.005

Hou LL , Zhang MZ , Zhao XD , et al. , 2018b . Stability of discrete-time switched systems with admissible edge-dependent switching signals . Int J Syst Sci , 49 ( 5 ): 974 - 983 . doi: 10.1080/00207721.2018.1439122 http://doi.org/10.1080/00207721.2018.1439122

Hua CC , Liu GP , Zhang L , et al. , 2019 . Cooperative stabilization for linear switched systems with asynchronous switching . IEEE Trans Syst Man Cybern Syst , 49 ( 6 ): 1081 - 1087 . doi: 10.1109/TSMC.2017.2721644 http://doi.org/10.1109/TSMC.2017.2721644

Li ZM , Chang XH , Park JH , 2021 . Quantized static output feedback fuzzy tracking control for discrete-time nonlinear networked systems with asynchronous event-triggered constraints . IEEE Trans Syst Man Cybern Syst , 51 ( 6 ): 3820 - 3831 . doi: 10.1109/TSMC.2019.2931530 http://doi.org/10.1109/TSMC.2019.2931530

Liberzon D , Morse AS , 1999 . Basic problems in stability and design of switched systems . IEEE Contr Syst , 19 ( 5 ): 59 - 70 . doi: 10.1109/37.793443 http://doi.org/10.1109/37.793443

Liu T , Wang C , 2019 . Quasi-time-dependent asynchronous <math id="M442"><mrow><msub><mi mathvariant="script">H</mi><mi>∞</mi></msub></mrow></math> control of discrete-time switched systems with mode-dependent persistent dwell-time . Eur J Contr , 48 : 66 - 73 . doi: 10.1016/j.ejcon.2018.11.002 http://doi.org/10.1016/j.ejcon.2018.11.002

Lu AY , Yang GH , 2020 . Stabilization of switched systems with all modes unstable via periodical switching laws . Automatica , 122 : 109150 . doi: 10.1016/j.automatica.2020.109150 http://doi.org/10.1016/j.automatica.2020.109150

Ren HL , Zong GD , Li TS , 2018 . Event-triggered finite-time control for networked switched linear systems with asynchronous switching . IEEE Trans Syst Man Cybern Syst , 48 ( 11 ): 1874 - 1884 . doi: 10.1109/TSMC.2017.2789186 http://doi.org/10.1109/TSMC.2017.2789186

Ren W , Xiong JL , 2016 . Stability and stabilization of switched stochastic systems under asynchronous switching . Syst Contr Lett , 97 : 184 - 192 . doi: 10.1016/j.sysconle.2016.09.005 http://doi.org/10.1016/j.sysconle.2016.09.005

Sang H , Nie H , 2018 . Asynchronous <math id="M443"><mrow><msub><mi>H</mi><mi>∞</mi></msub></mrow></math> control for discrete-time switched systems under state-dependent switching with dwell time constraint . Nonl Anal Hybrid Syst , 29 : 187 - 202 . doi: 10.1016/j.nahs.2018.01.007 http://doi.org/10.1016/j.nahs.2018.01.007

Shi S , Shi ZP , Fei ZY , 2019 . Asynchronous control for switched systems by using persistent dwell time modeling . Syst Contr Lett , 133 : 104523 . doi: 10.1016/j.sysconle.2019.104523 http://doi.org/10.1016/j.sysconle.2019.104523

Shorten R , Wirth F , Mason O , et al. , 2007 . Stability criteria for switched and hybrid systems . SIAM Rev , 49 ( 4 ): 545 - 592 . doi: 10.1137/05063516X http://doi.org/10.1137/05063516X

Wang B , Zhang HB , Wang G , et al. , 2014 . Asynchronous control of discrete-time impulsive switched systems with mode-dependent average dwell time . ISA Trans , 53 ( 2 ): 367 - 372 . doi: 10.1016/j.isatra.2013.11.019 http://doi.org/10.1016/j.isatra.2013.11.019

Wang XH , Zong GD , Sun HB , 2016 . Asynchronous finite-time dynamic output feedback control for switched time-delay systems with non-linear disturbances . IET Contr Theory Appl , 10 ( 10 ): 1142 - 1150 . doi: 10.1049/iet-cta.2015.0577 http://doi.org/10.1049/iet-cta.2015.0577

Wang YE , Zhao J , Jiang B , 2013 . Stabilization of a class of switched linear neutral systems under asynchronous switching . IEEE Trans Automat Contr , 58 ( 8 ): 2114 - 2119 . doi: 10.1109/TAC.2013.2250076 http://doi.org/10.1109/TAC.2013.2250076

Wang YE , Wu BW , Wu CY , 2017 . Stability and L 2 -gain analysis of switched input delay systems with unstable modes under asynchronous switching . J Franklin Inst , 354 ( 11 ): 4481 - 4497 . doi: 10.1016/j.jfranklin.2017.04.006 http://doi.org/10.1016/j.jfranklin.2017.04.006

Wang YQ , Xu N , Liu YJ , et al. , 2021 . Adaptive fault-tolerant control for switched nonlinear systems based on command filter technique . Appl Math Comput , 392 : 125725 . doi: 10.1016/j.amc.2020.125725 http://doi.org/10.1016/j.amc.2020.125725

Wu YY , Cao JD , Li QB , et al. , 2017 . Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching . Neur Netw , 85 : 128 - 139 . doi: 10.1016/j.neunet.2016.10.007 http://doi.org/10.1016/j.neunet.2016.10.007

Xiang WM , Xiao J , 2014 . Stabilization of switched continuous-time systems with all modes unstable via dwell time switching . Automatica , 50 ( 3 ): 940 - 945 . doi: 10.1016/j.automatica.2013.12.028 http://doi.org/10.1016/j.automatica.2013.12.028

Yang HY , Jiang YC , Yin S , 2018 . Fault-tolerant control of time-delay Markov jump systems with <math id="M444"><mrow><mi>I</mi><mi>t</mi><mover accent="true"><mi>o</mi><mo>^</mo></mover></mrow></math> stochastic process and output disturbance based on sliding mode observer . IEEE Trans Ind Inform , 14 ( 12 ): 5299 - 5307 . doi: 10.1109/TII.2018.2812754 http://doi.org/10.1109/TII.2018.2812754

Yang HY , Jiang YC , Yin S , 2021 . Adaptive fuzzy fault-tolerant control for Markov jump systems with additive and multiplicative actuator faults . IEEE Trans Fuzzy Syst , 29 ( 4 ): 772 - 785 . doi: 10.1109/TFUZZ.2020.2965884. http://doi.org/10.1109/TFUZZ.2020.2965884.

Yang JQ , Zhao XD , Bu XH , et al. , 2018 . Stabilization of switched linear systems via admissible edge-dependent switching signals . Nonl Anal Hybrid Syst , 29 : 100 - 109 . doi: 10.1016/j.nahs.2018.01.003 http://doi.org/10.1016/j.nahs.2018.01.003

Yu Q , Zhai GS , 2021 . A limit inferior <math id="M445"><mi>Φ</mi></math> -dependent average dwell time approach for stability analysis of switched systems . Int J Robust Nonl Contr , 31 ( 2 ): 565 - 581 . doi: 10.1002/rnc.5291. http://doi.org/10.1002/rnc.5291.

Yuan CZ , Wu F , 2015 . Hybrid control for switched linear systems with average dwell time . IEEE Trans Automat Contr , 60 ( 1 ): 240 - 245 . doi: 10.1109/TAC.2014.2322941 http://doi.org/10.1109/TAC.2014.2322941

Yuan S , Zhang LX , De Schutter B , et al. , 2018 . A novel Lyapunov function for a non-weighted L 2 gain of asynchronously switched linear systems . Automatica , 87 : 310 - 317 . doi: 10.1016/j.automatica.2017.10.018 http://doi.org/10.1016/j.automatica.2017.10.018

Zhang LX , Gao HJ , 2010 . Asynchronously switched control of switched linear systems with average dwell time . Automatica , 46 ( 5 ): 953 - 958 . doi: 10.1016/j.automatica.2010.02.021 http://doi.org/10.1016/j.automatica.2010.02.021

Zhang XL , Lin AH , Zeng JP , 2014 . Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems . J Zhejiang Univ-Sci C (Comput & Electron) , 15 ( 1 ): 31 - 42 . doi: 10.1631/jzus.C1300123 http://doi.org/10.1631/jzus.C1300123

Zhao XD , Zhang LX , Shi P , et al. , 2012 . Stability and stabilization of switched linear systems with mode-dependent average dwell time . IEEE Trans Automat Contr , 57 ( 7 ): 1809 - 1815 . doi: 10.1109/TAC.2011.2178629 http://doi.org/10.1109/TAC.2011.2178629

Zhao XD , Zhang LX , Shi P , et al. , 2014 . Robust control of continuous-time systems with state-dependent uncertainties and its application to electronic circuits . IEEE Trans Ind Electron , 61 ( 8 ): 4161 - 4170 . doi: 10.1109/TIE.2013.2286568 http://doi.org/10.1109/TIE.2013.2286568

Zhao XD , Yin S , Li HY , et al. , 2015 . Switching stabilization for a class of slowly switched systems . IEEE Trans Automat Contr , 60 ( 1 ): 221 - 226 . doi: 10.1109/TAC.2014.2322961 http://doi.org/10.1109/TAC.2014.2322961

Zhao XD , Yin YF , Zhang LX , et al. , 2016 . Control of switched nonlinear systems via T-S fuzzy modeling . IEEE Trans Fuzzy Syst , 24 ( 1 ): 235 - 241 . doi: 10.1109/TFUZZ.2015.2450834 http://doi.org/10.1109/TFUZZ.2015.2450834

Zhao XD , Kao YG , Niu B , et al. , 2017 . Control Synthesis of Switched Systems . Springer , Switzerland . doi: 10.1007/978-3-319-44830-5 http://doi.org/10.1007/978-3-319-44830-5

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