Fault detection filter design for Markov jump systems with persistent dwell-time

Zheng-Jin Zhang; Bin-Bin Gan; Zheng-Jin Zhang; Bin-Bin Gan

doi:10.3934/math.20251181

AIMS Mathematics

2025, Volume 10, Issue 11: 26867-26883. doi: 10.3934/math.20251181

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Fault detection filter design for Markov jump systems with persistent dwell-time

Zheng-Jin Zhang ^1,2,
Bin-Bin Gan ^{1,2
,
,}

1.
School of Automation, Qingdao University, Qingdao 266071, China
2.
Shandong Key Laboratory of Industrial Control Technology, Qingdao University, Qingdao 266071, China

Received: 26 September 2025 Revised: 05 November 2025 Accepted: 14 November 2025 Published: 20 November 2025
MSC : 93D30, 93C55, 93B70

This paper addresses the problem of fault detection (FD) for Markov jump systems (MJSs) with time-varying delays. The jumping property presented by system modes is described by the Markov chain and the transition probabilities of the Markov chain are described by adopting the more flexible persistent dwell-time (PDT) switching rule. By introducing a filter to establish a residual system, the problem was converted into an $ H_\infty $ filtering problem. The problem is complicated by the coexistence of time constraints in the PDT switching law and time-varying delays. By combining the Lyapunov-Krasovskii (L-K) method and switched system theory, a suitable filter was designed and a new PDT constraint was obtained. Ultimately, a virus mutation system model was used to demonstrate the practicability and effectiveness of the designed FD filter.
- Markov jump systems,
- fault detection filter,
- persistent dwell-time,
- time delays
Citation: Zheng-Jin Zhang, Bin-Bin Gan. Fault detection filter design for Markov jump systems with persistent dwell-time[J]. AIMS Mathematics, 2025, 10(11): 26867-26883. doi: 10.3934/math.20251181

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Abstract

This paper addresses the problem of fault detection (FD) for Markov jump systems (MJSs) with time-varying delays. The jumping property presented by system modes is described by the Markov chain and the transition probabilities of the Markov chain are described by adopting the more flexible persistent dwell-time (PDT) switching rule. By introducing a filter to establish a residual system, the problem was converted into an $ H_\infty $ filtering problem. The problem is complicated by the coexistence of time constraints in the PDT switching law and time-varying delays. By combining the Lyapunov-Krasovskii (L-K) method and switched system theory, a suitable filter was designed and a new PDT constraint was obtained. Ultimately, a virus mutation system model was used to demonstrate the practicability and effectiveness of the designed FD filter.

References

[1]	J. Wang, D. Wang, H. Yan, H. Shen, Composite antidisturbance $\mathcal{H}_{\infty}$ control for hidden Markov jump systems with multi-sensor against replay attacks, IEEE Trans. Autom. Control, 69 (2023), 1760–1766. https://doi.org/10.1109/TAC.2023.3326861 doi: 10.1109/TAC.2023.3326861
[2]	J. Wang, J. Wu, H. Shen, J. Cao, L. Rutkowski, Fuzzy $H_{\infty}$ control of discrete-time nonlinear Markov jump systems via a novel hybrid reinforcement $Q$-learning method, IEEE Trans. Cybern., 53 (2022), 7380–7391. https://doi.org/10.1109/TCYB.2022.3220537 doi: 10.1109/TCYB.2022.3220537
[3]	W. Fan, J. Yan, S. Huang, W. Liu, Research and prediction of opioid crisis based on BP neural network and Markov chain, AIMS Math., 4 (2019), 1357–1368. https://doi.org/10.3934/math.2019.5.1357 doi: 10.3934/math.2019.5.1357
[4]	X. Mao, W. Shan, J. Yu, Automatic diagnosis and subtyping of ischemic stroke based on a multi-dimensional deep learning system, IEEE Trans. Instrum. Meas., 73 (2024), 1–11. https://doi.org/10.1109/TIM.2024.3458059 doi: 10.1109/TIM.2024.3458059
[5]	H. Shen, F. Li, S. Xu, V. Sreeram, Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations, IEEE Trans. Autom. Control, 63 (2018), 2709–2714. https://doi.org/10.1109/TAC.2017.2774006 doi: 10.1109/TAC.2017.2774006
[6]	W. Lin, G. Tan, Q. Wang, J. Yu, Fault-tolerant state estimation for Markov jump neural networks with time-varying delays, IEEE Trans. Circuits Syst. II, 71 (2024), 2114–2118. https://doi.org/10.1109/TCSII.2023.3332390 doi: 10.1109/TCSII.2023.3332390
[7]	G. Tan, W. Chen, J. Yang, X. Tran, Z. Li, Dual control for autonomous airborne source search with Nesterov accelerated gradient descent: algorithm and performance analysis, Neurocomputing, 630 (2025), 129729. https://doi.org/10.1016/j.neucom.2025.129729 doi: 10.1016/j.neucom.2025.129729
[8]	C. Qin, W. Lin, J. Yu, Adaptive event-triggered fault detection for Markov jump nonlinear systems with time delays and uncertain parameters, Int. J. Robust Nonlinear Control, 34 (2024), 1939–1955. https://doi.org/10.1002/rnc.7062 doi: 10.1002/rnc.7062
[9]	G. Tan, T. Wang, A new result on $H_{\infty}$ filtering criterion based on improved techniques, Circuits Syst. Signal Process., 2025, 1–18. https://doi.org/10.1007/s00034-025-03305-4
[10]	L. Zhang, Y. Sun, Y. Pan, H. K. Lam, Reduced-order fault detection filter design for fuzzy semi-Markov jump systems with partly unknown transition rates, IEEE Trans. Syst. Man Cybern: Syst., 52 (2022), 7702–7713. https://doi.org/10.1109/TSMC.2022.3163719 doi: 10.1109/TSMC.2022.3163719
[11]	H. Shen, W. J. Lin, Z. Lian, Sampled-data stabilization of Markovian jumping conic-type nonlinear systems via an augmented looped functional, Commun. Nonlinear Sci. Numer. Simul., 147 (2025), 108814. https://doi.org/10.1016/j.cnsns.2025.108814 doi: 10.1016/j.cnsns.2025.108814
[12]	K. Yin, D. Yang, Asynchronous fault detection filter of positive Markov jump systems by dynamic event-triggered mechanism, ISA Trans., 138 (2023), 197–211. https://doi.org/10.1016/j.isatra.2023.03.017 doi: 10.1016/j.isatra.2023.03.017
[13]	A. S. Morse, Supervisory control of families of linear set-point controllers-Part Ⅰ. Exact matching, IEEE Trans. Autom. Control, 41 (1996), 1413–1431. https://doi.org/10.1109/9.539424 doi: 10.1109/9.539424
[14]	H. Geng, H. Zhang, A new $H_{\infty}$ control method of switched nonlinear systems with persistent dwell time: $H_{\infty}$ fuzzy control criterion with convergence rate constraints, AIMS Math., 9 (2024), 26092–26113. https://doi.org/10.3934/math.20241275 doi: 10.3934/math.20241275
[15]	S. Li, J. Lian, Almost sure stability of Markov jump systems with persistent dwell time switching, IEEE Trans. Syst. Man Cybern. Syst., 51 (2020), 6681–6690. https://doi.org/10.1109/TSMC.2020.2964034 doi: 10.1109/TSMC.2020.2964034
[16]	J. Wang, J. Wu, J. Cao, J. H. Park, H. Shen, $\mathcal{H}_{\infty}$ fuzzy dynamic output feedback reliable control for Markov jump nonlinear systems with PDT switched transition probabilities and its application, IEEE Trans. Fuzzy Syst., 30 (2021), 3113–3124. https://doi.org/10.1109/TFUZZ.2021.3104336 doi: 10.1109/TFUZZ.2021.3104336
[17]	W. Lin, Q. Han, X. Zhang, J. Yu, Reachable set synthesis of Markov jump systems with time-varying delays and mismatched modes, IEEE Trans. Circuits Syst. II, 69 (2021), 2186–2190. https://doi.org/10.1109/TCSII.2021.3126262 doi: 10.1109/TCSII.2021.3126262
[18]	W. Lin, Q. Wang, G. Tan, Asynchronous adaptive event-triggered fault detection for delayed Markov jump neural networks: a delay-variation-dependent approach, Neural Netw., 171 (2024), 53–60. https://doi.org/10.1016/j.neunet.2023.12.010 doi: 10.1016/j.neunet.2023.12.010
[19]	W. Liu, X. Fan, G. Tan, W. J. Lin, Reachable set control of cyber-physical systems with Markov jump parameters and hybrid attacks, IEEE Trans. Autom. Sci. Eng., 22 (2025), 18673–18681. https://doi.org/10.1109/TASE.2025.3589031 doi: 10.1109/TASE.2025.3589031
[20]	S. Jia, W. J. Lin, Adaptive event-triggered reachable set control for Markov jump cyber-physical systems with time-varying delays, AIMS Math., 9 (2024), 25127–25144. https://doi.org/10.3934/math.20241225 doi: 10.3934/math.20241225
[21]	G. Zhong, G. Yang, Simultaneous control and fault detection for discrete-time switched delay systems under the improved persistent dwell time switching, IET Control Theory Appl., 10 (2016), 814–824. https://doi.org/10.1049/iet-cta.2015.0925 doi: 10.1049/iet-cta.2015.0925
[22]	G. Göksu, U. Başer, Observer-based H$\infty$ finite-time control for switched linear systems with interval time-delay, Trans. Inst. Meas. Control, 41 (2019), 1348–1360. https://doi.org/10.1177/0142331218777559 doi: 10.1177/0142331218777559
[23]	H. Shen, Z. Huang, J. Cao, J. H. Park, Exponential $H_{\infty}$ filtering for continuous-time switched neural networks under persistent dwell-time switching regularity, IEEE Trans. Cybern., 50 (2019), 2440–2449. https://doi.org/10.1109/TCYB.2019.2901867 doi: 10.1109/TCYB.2019.2901867
[24]	A. Seuret, F. Gouaisbaut, Wirtinger-based integral inequality: application to time-delay systems, Automatica, 49 (2013), 2860–2866. https://doi.org/10.1016/j.automatica.2013.05.030 doi: 10.1016/j.automatica.2013.05.030
[25]	C. Zhang, Y. He, L. Jiang, M. Wu, Q. Wang, An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay, Automatica, 85 (2017), 481–485. https://doi.org/10.1016/j.automatica.2017.07.056 doi: 10.1016/j.automatica.2017.07.056
[26]	X. Zhang, Q. Han, A. Seuret, F. Gouaisbaut, Y. He, Overview of recent advances in stability of linear systems with time-varying delays, IET Control Theory Appl., 13 (2019), 1–16. https://doi.org/10.1049/iet-cta.2018.5188 doi: 10.1049/iet-cta.2018.5188
[27]	W. Qi, J. H. Park, J. Cheng, Y. Kao, X. Gao, Exponential stability and $\mathcal{L}_1$-gain analysis for positive time-delay Markovian jump systems with switching transition rates subject to average dwell time, Inf. Sci., 424 (2018), 224–234. https://doi.org/10.1016/j.ins.2017.10.008 doi: 10.1016/j.ins.2017.10.008

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