JZUS - Journal of Zhejiang University SCIENCE

Frontiers of Information Technology & Electronic Engineering 2022 Vol.23 No.5 P.810-822

http://doi.org/10.1631/FITEE.2000698

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

Author(s): Linlin HOU, Xuan MA, Haibin SUN
Affiliation(s): School of Computer Science, Qufu Normal University, Rizhao 276826, China; more
Corresponding email(s): houtingting8706@126.com, maxuan24@163.com, fengyun198212@163.com
Key Words: Asynchronous switching, Admissible edge-dependent average dwell time, Multi-Lyapunov function

Share this article to： More <<< Previous Article \|

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.

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

侯林林¹，马萱¹，孙海滨²
¹曲阜师范大学计算机学院，中国日照市，276826
²曲阜师范大学工学院，中国日照市，276826
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。

关键词：异步切换；可容许边依赖平均驻留时间；多李雅普诺夫函数

Reference

[1]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.

[2]Deaecto GS, Geromel JC, Daafouz J, 2011. Dynamic output feedback H_inf control of switched linear systems. Automatica, 47(8):1713-1720.

[3]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.

[4]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.

[5]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.

[6]Hespanha JP, Morse AS, 1999. Stability of switched systems with average dwell-time. Proc 38^th IEEE Conf on Decision Control, p.2655-2660.

[7]Hou LL, Zhao XD, Sun HB, et al., 2018a. l₂−l_∞ filtering of discrete-time switched systems via admissible edge-dependent switching signals. Syst Contr Lett, 113:17-26.

[8]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.

[9]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.

[10]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.

[11]Liberzon D, Morse AS, 1999. Basic problems in stability and design of switched systems. IEEE Contr Syst, 19(5):59-70.

[12]Liu T, Wang C, 2019. Quasi-time-dependent asynchronous H_∞ control of discrete-time switched systems with mode-dependent persistent dwell-time. Eur J Contr, 48:66-73.

[13]Lu AY, Yang GH, 2020. Stabilization of switched systems with all modes unstable via periodical switching laws. Automatica, 122:109150.

[14]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.

[15]Ren W, Xiong JL, 2016. Stability and stabilization of switched stochastic systems under asynchronous switching. Syst Contr Lett, 97:184-192.

[16]Sang H, Nie H, 2018. Asynchronous H_∞ control for discrete-time switched systems under state-dependent switching with dwell time constraint. Nonl Anal Hybrid Syst, 29:187-202.

[17]Shi S, Shi ZP, Fei ZY, 2019. Asynchronous control for switched systems by using persistent dwell time modeling. Syst Contr Lett, 133:104523.

[18]Shorten R, Wirth F, Mason O, et al., 2007. Stability criteria for switched and hybrid systems. SIAM Rev, 49(4):545-592.

[19]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.

[20]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.

[21]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.

[22]Wang YE, Wu BW, Wu CY, 2017. Stability and L₂-gain analysis of switched input delay systems with unstable modes under asynchronous switching. J Franklin Inst, 354(11):4481-4497.

[23]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.

[24]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.

[25]Xiang WM, Xiao J, 2014. Stabilization of switched continuous-time systems with all modes unstable via dwell time switching. Automatica, 50(3):940-945.

[26]Yang HY, Jiang YC, Yin S, 2018. Fault-tolerant control of time-delay Markov jump systems with Itô stochastic process and output disturbance based on sliding mode observer. IEEE Trans Ind Inform, 14(12):5299-5307.

[27]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.

[28]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.

[29]Yu Q, Zhai GS, 2021. A limit inferior Φ-dependent average dwell time approach for stability analysis of switched systems. Int J Robust Nonl Contr, 31(2):565-581.

[30]Yuan CZ, Wu F, 2015. Hybrid control for switched linear systems with average dwell time. IEEE Trans Automat Contr, 60(1):240-245.

[31]Yuan S, Zhang LX, De Schutter B, et al., 2018. A novel Lyapunov function for a non-weighted L₂ gain of asynchronously switched linear systems. Automatica, 87:310-317.

[32]Zhang LX, Gao HJ, 2010. Asynchronously switched control of switched linear systems with average dwell time. Automatica, 46(5):953-958.

[33]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.

[34]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.

[35]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.

[36]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.

[37]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.

[38]Zhao XD, Kao YG, Niu B, et al., 2017. Control Synthesis of Switched Systems. Springer, Switzerland.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Similar articles

- Go to

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

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference