This paper investigates the issues of finite-time - boundedness and resilient control for a class of Semi-Markov jump systems (SMJSs) with disturbances. By conducting an analysis on the finite-time - boundedness of stochastic SMJSs, we established a series of sufficient conditions to ensure the desired boundedness property. In light of uncertainties present in both the system dynamics and the external environment, mode-dependent resilient controllers are proposed for the boundedness of the uncertain system. The system’s modal switching is regulated by an SMJS. The developed resilient control strategy is designed to attenuate the peak magnitude of the system output, thereby attenuating or even eliminating the detrimental effects caused by abrupt external disturbances. Finally, a numerical example of a quadrotor unmanned aerial vehicle (UAV) altitude control system is included to illustrate the performance of the presented control strategy.
BarlowRProschanFHunterL (1996) Mathematical Theory of Reliability. Society for Industrial and Applied Mathematics.
2.
CaoZRNiuYGSongJ (2020) Finite-time sliding-mode control of Markovian jump cyber-physical systems against randomly occurring injection attacks. IEEE Transactions on Automatic Control65(3): 1264–1271. https://doi.org/10.1109/TAC.2019.2926156
3.
ChenMLiY (2019) Model reference resilient control for the helicopter with time-varying disturbance. International Journal of Robust and Nonlinear Control29: 5095–5117. https://doi.org/10.1002/rnc.4665
4.
DingXLiH (2020) Finite-time time-variant feedback stabilization of logical control networks with Markov jump disturbances. IEEE Transactions on Circuits and Systems II: Express Briefs67(10): 2079–2083. https://doi.org/10.1109/TCSII.2019.2949558
5.
DoratoP (1961) Short time stability in linear time-varying systems. In: Proceedings of the IRE international convention record part, New York, 9 May 1961, pp.83–87.
6.
GriffoAWangJ (2012) Modeling and stability analysis of hybrid power systems for the more electric aircraft. Electric Power Systems Research82: 59–67. https://doi.org/10.1016/j.epsr.2011.08.017
7.
HarishSMichaelG (2018) Relaxed autonomously switched hybrid system approach to indirect multiphase aerospace trajectory optimization. Journal of Spacecraft and Rockets55(3): 611–621. https://doi.org/10.2514/1.A34012
8.
HeHQiWLiuZ, et al. (2021) Adaptive attack-resilient control for Markov jump system with additive attacks. Nonlinear Dynamics103: 1585–1598. https://doi.org/10.1007/s11071-020-06085-5
9.
LiCXuRLiuZ, et al. (2025) Adaptive finite-time neural control for uncertain Markov jump systems with actuator faults. Circuits, Systems, and Signal Processing44: 03074. https://doi.org/10.1007/s00034-025-03074-0
10.
LiuQXuSLuC (2020) Early recognition of driving intention for lane change based on recurrent hidden semi-Markov model. IEEE Transactions on Vehicular Technology69(10): 10545–10557. https://doi.org/10.1109/TVT.2020.3011672
11.
MahmoudMJiangJZhangY (2001) Stochastic stability analysis of fault-tolerant control systems in the presence of noise. IEEE Transactions on Automatic Control46(11): 1810–1815. https://doi.org/10.1109/9.964697
12.
PanKYangFFengZ, et al. (2023) Attack estimation-based resilient control for cyber-physical power systems. Transactions of the Institute of Measurement and Control45: 886–898. https://doi.org/10.1177/01423312221122471
13.
PanSXieXZhuY, et al. (2024) Resilient and finite-time H∞ control of semi-Markov jump systems with both upper and lower thresholds of sojourn time. International Journal of Robust and Nonlinear Control34: 6542–6561. https://doi.org/10.1002/rnc.7284
14.
PangHGaoXLiC (2025) Robust finite-time passivity and stabilization of uncertain switched nonlinear system with no finite-time passive subsystems. Transactions of the Institute of Measurement and Control. Epub ahead of print 29 July. https://doi.org/10.1177/01423312251344662
15.
QiWZongGZhengWX (2021) Adaptive event-triggered SMC for stochastic switching systems with semi-Markov process and application to boost converter circuit model. IEEE Transactions on Circuits and Systems I: Regular Papers68(2): 786–796. https://doi.org/10.1109/TCSI.2020.3036847
16.
QiWHZongGDAhnCK (2022) Input-output finite-time asynchronous SMC for nonlinear semi-Markov switching systems with application. IEEE Transactions on Systems, Man, and Cybernetics: Systems52(8): 5344–5353. https://doi.org/10.1109/TSMC.2021.3122965
17.
QiuLTengJChenR, et al. (2025) Robust control strategy for networked semi-Markov jump system with random delay. International Journal of Robust and Nonlinear Control35: e7855. https://doi.org/10.1002/rnc.7855
18.
RanGTLiuJLiCJ (2023) Finite-time filtering for fuzzy nonlinear semi-Markov jump systems with deception attacks and a periodical transmission. Journal of the Franklin Institute360(16): 12576–12597. https://doi.org/10.1016/j.jfranklin.2021.07.055
19.
SangHZhaoJ (2022) Finite-time H∞ estimator design for switched discrete-time delayed neural networks with event-triggered strategy. IEEE Transactions on Cybernetics52(3): 1713–1725. https://doi.org/10.1109/TCYB.2020.2992518
20.
ShenHZhangZLiF (2024) Non-fragile H∞ control for piecewise homogeneous hidden semi-Markov Lur’e systems. IEEE Transactions on Circuits and Systems II: Express Briefs71(1): 306–310. https://doi.org/10.1109/TCSII.2023.3300096
21.
ShiYZhaoJSunX (2021) A bumpless transfer control strategy for switched systems and its application to an aero-engine. IEEE Transactions on Industrial Informatics17(1): 52–62. https://doi.org/10.1109/TII.2020.2979736
22.
SunJHuYChaiY (2015) l∞ event-triggered networked control under time-varying communication delay with communication cost reduction. Journal of the Franklin Institute352: 4776–4800. https://doi.org/10.1016/j.jfranklin.2015.07.016
23.
WanCYangZZhangD, et al. (2018) Resilience in transportation systems: A systematic review and future directions. Transport Reviews38(4): 479–498. https://doi.org/10.1080/01441647.2017.1383532
24.
WangJZhangYSuL (2022) Model-based fuzzy Ly–L∞ filtering for discrete-time semi-Markov jump nonlinear systems using semi-Markov Kernel. IEEE Transactions on Fuzzy Systems30(7): 2289–2299. https://doi.org/10.1109/TFUZZ.2021.3078832
25.
WangJMMaSPZhangCH (2019) Finite-time H∞ control for TS fuzzy descriptor semi-Markov jump systems via static output feedback. Fuzzy Sets and Systems365: 60–80. https://doi.org/10.1016/j.fss.2018.04.001
26.
WangYXiaYShenH, et al. (2018) SMC design for robust stabilization of nonlinear Markovian jump singular systems. IEEE Transactions on Automatic Control63(1): 219–224. https://doi.org/10.1109/TAC.2017.2720970
27.
WeissLInfanteEF (1967) Finite time stability under perturbing forces and on product spaces. IEEE Transactions on Automatic Control12(1): 54–59
28.
XiaYLiMShiP, et al. (2017) Finite-time stability for networked control systems with communication delays and packet dropouts. Transactions of the Institute of Measurement and Control39(9): 1421–1431. https://doi.org/10.1177/0142331215624400
29.
XieLFuMde SouzaCE (1992) H∞ control and quadratic stabilization of systems with parameter uncertainty via output feedback. IEEE Transactions on Automatic Control37(8): 1253–1256. https://doi.org/10.1109/9.151120
30.
XuZWWuZGSuHY (2020) Energy-to-peak filtering of semi-Markov jump systems with mismatched modes. IEEE Transactions on Automatic Control65(10): 4356–4361. https://doi.org/10.1109/TAC.2019.2955014
31.
YaoKChenKMaoC, et al. (2021) Optimal switching frequency variation range control for critical conduction mode boost power factor correction converter. IEEE Transactions on Industrial Electronics68(2): 1197–1209. https://doi.org/10.1109/TIE.2020.2969111
32.
ZhangLLengYColaneriP (2016) Stability and stabilization of discrete-time semi-Markov jump linear systems via semi-Markov Kernel approach. IEEE Transactions on Automatic Control61: 503–508. https://doi.org/10.1109/TAC.2015.2438424
