Considering that the perturbation of controller parameters may cause severe performance deterioration in practice, this work is focused on asynchronous resilient H∞ control for discrete-time switched systems under average dwell time switching. The multiple non-monotonic Lyapunov function approach is employed to analyze the stability and H∞ performance to reduce the conservation level. First, an H∞ stability criterion is derived for general switched nonlinear systems, based on which a sufficient condition is further obtained for the resultant closed-loop system under asynchronous average dwell time switching. Then, a synthesis condition for a resilient output-feedback H∞ controller is developed using Fensler’s lemma. Finally, the effectiveness and advantages of the proposed controller design method are demonstrated by two simulated examples.
LiberzonD.Switching in systems and control. Boston, MA: Springer, 2003.
2.
BranickyMS.Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans Autom Control1998; 43(4): 475–482.
3.
WangMZhaoJDimirovskiGM. control for a class of cascade switched nonlinear systems. Asian J Control2008; 10(6): 724–729.
4.
Mancilla-AguilarJL.A condition for the stability of switched nonlinear systems. IEEE Trans Autom Control2000; 45(11): 2077–2079.
5.
WangYESunXMMazencF.Stability of switched nonlinear systems with delay and disturbance. Automatica2016; 69: 78–86.
6.
ZhaoXZhangLShiP, et al. Stability of switched positive linear systems with average dwell time switching. Automatica2012; 48(6): 1132–1137.
7.
YuanCWuF.Hybrid control for switched linear systems with average dwell time. IEEE Trans Autom Control2014; 60(1): 240–245.
8.
SuQWangPLiJ, et al. Stabilization of discrete-time switched systems with state constraints based on mode-dependent average dwell time. Asian J Control2017; 19(1): 67–73.
9.
AllerhandLIShakedU.Robust stability and stabilization of linear switched systems with dwell time. IEEE Trans Autom Control2010; 56(2): 381–386.
10.
AhmadiAA.Non-monotonic Lyapunov functions for stability of nonlinear and switched systems: theory and computation. PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA, 2008.
11.
DerakhshanSFFatehiA.Non-monotonic Lyapunov functions for stability analysis and stabilization of discrete time Takagi-Sugeno fuzzy systems. Int J Innov Comput Inform Control2014; 10(4): 1567–1586.
12.
XieYWenJNguangSK, et al. Stability, -gain, and robust control for switched systems via -step ahead Lyapunov function approach. IEEE Access 2017; 5: 26400–26408.
13.
WenJNguangSKShiP, et al. Stability and control of discrete-time switched systems via one-step ahead Lyapunov function approach. IET Control Theor Appl2018; 12(8): 1141–1147.
14.
LacerdaMJGomideTDS. Stability and stabilisability of switched discrete-time systems based on structured Lyapunov functions. IET Control Theor Appl2020; 14(5): 781–789.
15.
LacerdaMJSeilerP.Stability of uncertain systems using Lyapunov functions with non-monotonic terms. Automatica2017; 82: 187–193.
16.
ZhangLGaoH.Asynchronously switched control of switched linear systems with average dwell time. Automatica2010; 46(5): 953–958.
17.
JiangZYanP. output-feedback control for discrete-time switched linear systems via asynchronous switching. J Frankl Inst2018; 355(14): 6215–6238.
18.
ZhangHWangBXieD, et al. Stability, -gain and asynchronous control for continuous-time switched systems. Int J Robust Nonlin Control2015; 25(4): 575–587.
19.
RiegerCGGertmanDIMcQueenMA. Resilient control systems: next generation design research. In: Proceedings of the 2009 2nd conference on human system interactions, Catania, 21–23 May 2009, pp. 632–636. New York: IEEE.
20.
ZhuKSongYDingD.Resilient RMPC for polytopic uncertain systems under TOD protocol: a switched system approach. Int J Robust Nonlin Control2018; 28(16): 5103–5117.
21.
LuXYangLWangH, et al. Resilient asynchronous control designed for discrete-time Markov jump systems: static output feedback case. Adv Mech Eng2018; 10(1): 7747709.
22.
HeSAiQRenC, et al. Finite-time resilient controller design of a class of uncertain nonlinear systems with time-delays under asynchronous switching. IEEE Trans Syst Man Cyb Syst2018; 49(2): 281–286.
23.
YuanYSunFZhuQ.Resilient control in the presence of dos attack: switched system approach. Int J Control Autom Syst2015; 13: 1423–1435.
24.
LianJHuangX.Resilient control of networked switched systems against DOS attack. IEEE Trans Ind Inform2021; 18(4): 2354–2363.
25.
FangLLinHAntsaklisPJ.Stabilization and performance analysis for a class of switched systems. In: Proceedings of the 2004 43rd IEEE conference on decision and control (CDC) (IEEE Cat. No. 04CH37601), Nassau, Bahamas, 14–17 December 2004, vol. 3, pp. 3265–3270. New York: IEEE.
26.
ZhangLShiP.Stability, -gain and asynchronous control of discrete-time switched systems with average dwell time. IEEE Trans Autom Control2009; 54(9): 2192–2199.
27.
ZhangLCuiNLiuM, et al. Asynchronous filtering of discrete-time switched linear systems with average dwell time. IEEE Trans Circ Syst I Reg Pap2010; 58(5): 1109–1118.
