This article considers the finite-time control problem for singular Markovian jump systems with time-varying delay subject to input saturation. Considering the discontinuities caused by the mode-dependent singular matrix and Markovian jump switching behavior, the result of this article is more practical. First, a hidden model-based state feedback controller is designed to guarantee that the considered system is mean-square locally finite-time stabilizable by employing an appropriate Lyapunov function. Second, some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities which considers the time-varying delay and input saturation. Finally, the correctness of the proposed method is verified by three numerical examples.
ShenHLiFXuSY, et al. Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations. IEEE T Autom Contr2018; 63(8): 2709–2714.
2.
ShenHLiFWuZG, et al. Fuzzy-model-based non-fragile control for nonlinear singularly perturbed systems with semi-Markov jump parameters. IEEE T Fuzzy Syst2018; 26(6): 3428–3439.
3.
ShenHMenYZWuZG, et al. Nonfragile control for fuzzy Markovian jump systems under fast sampling singular perturbation. IEEE T Syst Man Cyber: Syst2018; 48(12): 2058–2069.
4.
ShenHHuoSCCaoJD, et al. Generalized state estimation for Markovian coupled networks under round-robin protocol and redundant channels. IEEE T Cyber2019; 49(4): 1292–1301.
5.
ZhongTLiuF.H∞ control discrete-time descriptor systems with Markov jumping parameters. J Xidian Univ2008; 35(5): 951–956.
6.
ShenHXingMPYanHC, et al. Observer-based control for singularly perturbed semi-Markov jump systems with an improved weighted TOD protocol. Sci China Inform Sci2022; 65(9): 199–204.
7.
WangGLXuL.Almost sure stability and stabilization of Markovian jump linear systems with stochastic switching. IEEE T Autom Contr2022; 67(3): 1529–1536.
8.
WangYYPuHYShi Pen KiAhnC, et al. Sliding mode control for singularly perturbed Markov jump descriptor systems with nonlinear perturbation. Automatica2021; 127: 109515.
9.
HeSLiuF.Robust peak-to-peak filtering for Markov jump systems. Sig Peocess2010; 90(2): 513–522.
10.
XuSYLamJMaoXR.Delay-dependent H∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE T Circ Syst I: Reg Pap2007; 54(9): 2070–2077.
11.
WuZGDongSShiP, et al. Reliable filtering of nonlinear Markovian jump systems: the continuous-time case. IEEE T Syst Man Cyber Syst2019; 49(2): 386–394.
12.
ShenHMenYZWuZG, et al. Network-based quantized control for fuzzy singularly perturbed semi-Markov jump systems and its application. IEEE T Circ Syst I: Reg Pap2019; 66(3): 1130–1140.
13.
GaoJZhaoZWangJ, et al. Event-triggered output feedback control for discrete Markov jump systems under deception attack. J Frankl Inst2020; 357: 6435–6452.
14.
LianJLiSLiuJ.T-S fuzzy control of positive Markov jump nonlinear systems. IEEE T Fuzzy Syst2018; 26(4): 374–2383.
15.
KavikumarRSakthivelRKwonOM, et al. Reliable non-fragile memory state feedback controller design for fuzzy Markov jump systems. Nonl Anal Hybrid Syst2020; 35: 100828.
16.
DongSWuZGSuH.Asynchronous control of continuous-time nonlinear Markov jump systems subject to strict dissipativity. IEEE T Autom Contr2018; 64(3): 1250–1256.
17.
ChengJAhnCKKarimiHR, et al. An event-based asynchronous approach to Markov jump systems with hidden mode detections and missing measurements. IEEE T Syst Man Cyber Syst2018; 49(9): 1749–1758.
18.
DongSWuZGPanYG.Hidden-Markov-model-based asynchronous filter design of nonlinear Markov jump systems in continuous-time domain. IEEE T Cyber2018; 49(6): 294–2304.
19.
DongSChenCFangM, et al. Dissipativity-based asynchronous fuzzy sliding mode control for T-S fuzzy hidden Markov jump systems. IEEE T Cyber2020; 50(9): 4020–4030.
20.
XueMYanHZhangH, et al. Hidden-Markov-model-based asynchronous H-infinity tracking control of fuzzy Markov jump systems. IEEE T Fuzzy Syst2020; 29(5): 1081–1092.
21.
HeSLiuF.Finite-time fuzzy control of nonlinear jump system with time delays via dynamic observer-based state feedback. IEEE T Fuzzy Syst2012; 20(4): 605–614.
22.
WangJMaSZhangC.Finite-time H∞ filtering for nonlinear singular systems with nonhomogeneous Markov jumps. IEEE T Cyber2018; 49(6): 2133–2143.
23.
GuanWLiuF.Finite-time dissipative control for singular T-S fuzzy Markovian jump systems under actuator saturation with partly unknown transition rates. Neurocomputing2016; 27: 60–70.
24.
ShenHLiFYanH, et al. Finite-time event-triggered H∞ control for T-S fuzzy Markov jump systems. IEEE T Fuzzy Syst2018; 26(5): 3122–3135.
25.
WeiJZhangXZhiH, et al. New finite-time stability conditions of linear discrete switched singular systems with finite time unstable subsystem. J Frankl Inst2020; 357(1): 279–293.
26.
XuSYLamJ.Robust control and filtering of singular systems. Berlin: Springer, 2006.
27.
KwonNKParkISParkP.Dynamic output-feedback control for singular Markovian jump system: LMI approach. IEEE T Autom Contr2017; 62: 5396–5400.
28.
KwonNKParkISParkP. H control for singular Markovian jump systems with incomplete knowledge of transition probabilities. Appl Math Comput2017; 295: 126–135.
29.
LiuYFMaYCWangYN.Reliable sliding mode finite-time control for discrete-time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities. Int J Robust Nonl Contr2017; 28(2): 4–7.
30.
ZhangQZhangJWangY.Sliding-mode control for singular Markovian jump systems with Brownian motion based on stochastic sliding mode surface. IEEE T Syst Man Cyber Syst2019; 49(3): 494–505.
31.
LiLZhangQZhuB.Fuzzy stochastic optimal guaranteed cost control of bio-economic singular Markovian jump systems. IEEE T Cyber2015; 45(11): 2512–2521.
32.
CuiYShenJFengZ, et al. Stability analysis for positive singular systems with time-varying delays. IEEE T Autom Contr2017; 63(5): 1487–1494.
33.
CaoYLinXWardDG.Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances. Automatica2004; 40(7): 1221–1228.
34.
CorradiniMLOrlandoG.Linear unstable plants with saturating actuators: robust stabilization by a time varying sliding surface. Automatica2007; 43(1): 88–94.
35.
ChousIXiangZ.H stabilization of 2-D discrete switched delayed systems represented by the Roesser model subject to actuator saturation. Trans Inst Meas Contr2015; 37(10): 1242–1253.
36.
DuanZXGhousIAkhtarJ.Robust L2-L filter design for uncertain 2-D continuous nonlinear delayed systems with saturation. IEEE Access2018; 6: 73647–73658.
37.
SongXNXuSY.Robust stabilization of state delayed T-S fuzzy systems with input saturation via dynamic anti-windup fuzzy design. Int J Innov Comput Inf Contr2011; 7(12): 6665–6676.
38.
LiSLianJ.Hidden Markov model based control for singular Markov jump systems. J Frank Inst2021; 358: 4141–4158.
39.
ZhouLDanielWHZhaiG.Stability analysis of switched linear singular systems. Automatica2013; 49(5): 1481–1487.
40.
XiaoXParkJHZhouL.New results on stability analysis of Markovian switching singular systems. IEEE T Autom Contr2018; 64(5): 2084–2091.
