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Asynchronous Hybrid \(H_\infty \) Filtering for Uncertain Impulsive Switched Systems

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Abstract

This article addresses the hybrid \(H_\infty \) filtering problem for continuous-time uncertain linear impulsive switched systems with the asynchronous switching. Unlike most work about filtering problems, this article ponders multiple state impulsive jumps in the whole switched systems. In other words, the state impulsive jumps take place in subsystem switching instants as well as in filter switching instants, which add challenges to the \(H_\infty \) filtering problem considered in this article. In the filter design, one has to take account of the asynchronous switching, which hints that the switching of the subsystem and its corresponding filter does not occur concurrently. The average dwell time approach is applied to design the switching rule. This article focuses on the design of the hybrid \(H_\infty \) filter that can keep the filtering error systems globally uniformly asymptotically stable with \(H_\infty \) performance index. By constructing Lyapunov-like functions that allow the increment during the asynchronous period and in the state jump instants, sufficient conditions for the expected hybrid \(H_\infty \) filter are obtained in the form of linear matrix inequalities. At last, an example is offered to demonstrate the applications of the acquired theorems.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. X.H. Chang, Robust nonfragile \(H_\infty \) filtering of fuzzy systems with linear fractional parametric uncertainties. IEEE Trans. Fuzzy Syst. 20(6), 1001–1011 (2012). https://doi.org/10.1109/TFUZZ.2012.218729

    Article  MathSciNet  Google Scholar 

  2. X.H. Chang, Q. Liu, Y.M. Wang, J. Xiong, Fuzzy peak-to-peak filtering for networked nonlinear systems with multipath data packet dropouts. IEEE Trans. Fuzzy Syst. 27(3), 436–446 (2019). https://doi.org/10.1109/TFUZZ.2018.2859903

    Article  Google Scholar 

  3. X.H. Chang, L. Zhang, J.H. Park, Robust static output feedback \(H_\infty \) control for uncertain fuzzy systems. Fuzzy Sets Syst. 273, 87–104 (2015). https://doi.org/10.1016/j.fss.2014.10.023

    Article  Google Scholar 

  4. J. Cheng, Y.Y. Wu, H.C. Yan, Z.G. Wu, K.B. Shi, Protocol-based filtering for fuzzy Markov affine systems with switching chain. Automatica 141, 110321 (2022). https://doi.org/10.1016/j.automatica.2022.110321

    Article  MathSciNet  Google Scholar 

  5. G. Conte, A.M. Perdon, E. Zattoni, Disturbance decoupling with stability for impulsive switching linear systems. IFAC-PapersOnLine 52(17), 19–24 (2019). https://doi.org/10.1016/j.ifacol.2019.11.020

    Article  MathSciNet  Google Scholar 

  6. Y.G. Fan, M. Wang, H. Fu, B. Zhang, Y.C. Bian, G.H. Sun, Quasi-time-dependent \(H_\infty \) filtering of discrete-time 2-D switched systems with mode-dependent persistent dwell time. Circuits Syst. Signal Process. 40(12), 5886–5912 (2021). https://doi.org/10.1007/s00034-021-01746-1

    Article  Google Scholar 

  7. G.Z. Feng, J.D. Cao, Stability analysis of impulsive switched singular systems. IET Control Theory Appl. 9(6), 863–870 (2015). https://doi.org/10.1049/iet-cta.2013.1142

    Article  MathSciNet  Google Scholar 

  8. H. Gao, K.B. Shi, H.B. Zhang, Event-triggered finite-time \(H_\infty \) filtering for a class of switched nonlinear systems via the T–S fuzzy model. Circuits Syst. Signal Process. 40(7), 3161–3178 (2021). https://doi.org/10.1007/s00034-020-01619-z

    Article  Google Scholar 

  9. H.J. Gao, C.H. Wang, Delay-dependent robust \(H_\infty \) and \(L_2-L_\infty \) filtering for a class of uncertain nonlinear time-delay systems. IEEE Trans. Autom. Control 48(9), 1661–1666 (2003). https://doi.org/10.1109/TAC.2003.817012

    Article  Google Scholar 

  10. É. Gyurkovics, T. Takács, Robust energy-to-peak filter design for a class of unstable polytopic systems with a macroeconomic application. Appl. Math. Comput. 420, 126729 (2022). https://doi.org/10.1016/j.amc.2021.126729

    Article  MathSciNet  Google Scholar 

  11. J.P. Hespanha, A.S. Morse, Stability of switched systems with average dwell-time, in Proceedings of the 38th IEEE Conference on Decision and Control(Cat. No.99CH36304), vol 3 (1999), pp 2655–2660. https://doi.org/10.1109/CDC.1999.831330

  12. J. Hu, Z.D. Wang, G.P. Liu, Delay compensation-based state estimation for time-varying complex networks with incomplete observations and dynamical bias. IEEE Trans. Cybern. 52(11), 12071–12083 (2022). https://doi.org/10.1109/TCYB.2020.3043283

    Article  PubMed  Google Scholar 

  13. Y. Kang, N.K. Zhang, G.Y. Chen, Global exponential stability of impulsive switched positive nonlinear systems with mode-dependent impulses. Appl. Math. Comput. 436, 127515 (2023). https://doi.org/10.1016/j.amc.2022.127515

    Article  MathSciNet  Google Scholar 

  14. J. Li, Q.X. Zhu, Stability of neutral stochastic delayed systems with switching and distributed-delay dependent impulses. Nonlinear Anal. Hybrid Syst. 47, 101279 (2023). https://doi.org/10.1016/j.nahs.2022.101279

    Article  MathSciNet  Google Scholar 

  15. P. Li, X.D. Li, J.Q. Lu, Input-to-state stability of impulsive delay systems with multiple impulses. IEEE Trans. Autom. Control 66(1), 362–368 (2021). https://doi.org/10.1109/TAC.2020.2982156

    Article  MathSciNet  Google Scholar 

  16. X. Li, Z.R. Xiang, H.R. Karimi, Asynchronously switched control of discrete impulsive switched systems with time delays. Inf. Sci. 249, 132–142 (2013). https://doi.org/10.1016/j.ins.2013.06.007

    Article  ADS  Google Scholar 

  17. X.D. Li, P. Li, Q.G. Wang, Input/output-to-state stability of impulsive switched systems. Syst. Control Lett. 116, 1–7 (2018). https://doi.org/10.1016/j.sysconle.2018.04.001

    Article  MathSciNet  CAS  Google Scholar 

  18. Y. Li, H.B. Zhang, Asynchronous \(H_\infty \) control of switched uncertain discrete-time fuzzy systems via basis-dependent multiple Lyapunov functions approach. Circuits Syst. Signal Process. 37(1), 135–162 (2018). https://doi.org/10.1007/s00034-017-0550-5

    Article  MathSciNet  Google Scholar 

  19. J. Lian, C.W. Mu, P. Shi, Asynchronous \(H_\infty \) filtering for switched stochastic systems with time-varying delay. Inf. Sci. 224, 200–212 (2013). https://doi.org/10.1016/j.ins.2012.10.009

    Article  MathSciNet  Google Scholar 

  20. J. Liu, K. Yin, D.D. Yang, H.C. Li, Stability analysis of switched positive systems with an impulse interval. Circuits Syst. Signal Process. 40(2), 1005–1020 (2021). https://doi.org/10.1007/s00034-020-01495-7

    Article  Google Scholar 

  21. S. Lu, W.H. Zhang, Robust \(H_\infty \) filtering and control for a class of linear systems with fractional stochastic noise. Phys. A-Stat. Mech. ITS Appl. 526, 120958 (2019). https://doi.org/10.1016/j.physa.2019.04.194

    Article  MathSciNet  Google Scholar 

  22. J.J. Ren, X.Z. Liu, H. Zhu, S.M. Zhong, C. Wu, Exponential \(H_\infty \) synchronization of switching fuzzy systems with time-varying delay and impulses. Fuzzy Sets Syst. 365, 116–139 (2019). https://doi.org/10.1016/j.fss.2018.05.019

    Article  MathSciNet  Google Scholar 

  23. H. Shen, X.M. Liu, J.W. Xia, X.Y. Chen, J. Wang, Finite-time energy-to-peak fuzzy filtering for persistent dwell time switched nonlinear systems with unreliable links. Inf. Sci. 579, 293–309 (2021). https://doi.org/10.1016/j.ins.2021.07.081

    Article  MathSciNet  Google Scholar 

  24. P.W. Shi, W.C. Sun, X.B. Yang, I.J. Rudas, H.J. Gao, Master-slave synchronous control of dual-drive gantry stage with cogging force compensation. IEEE Trans. Syst. Man Cybern. Syst. 53(1), 216–225 (2023). https://doi.org/10.1109/TSMC.2022.3176952

    Article  Google Scholar 

  25. P.W. Shi, X.H. Yu, X.B. Yang, J.J. Rodríguez-Andina, W.C. Sun, H.J. Gao, Composite adaptive synchronous control of dual-drive gantry stage with load movement. IEEE Open J. Ind. Electron. Soc. 4, 63–74 (2023). https://doi.org/10.1109/OJIES.2022.3233848

    Article  Google Scholar 

  26. S. Shi, Z.Y. Fei, T. Wang, Y.L. Xu, Filtering for switched T-S fuzzy systems with persistent dwell time. IEEE Trans. Cybern. 49(5), 1923–1931 (2019). https://doi.org/10.1109/TCYB.2018.2816982

    Article  PubMed  Google Scholar 

  27. M. Souza, A.R. Fioravanti, M. Corless, R.N. Shorten, Switching controller design with dwell-times and sampling. IEEE Trans. Autom. Control 62(11), 5837–5843 (2017). https://doi.org/10.1109/TAC.2016.2640022

    Article  MathSciNet  Google Scholar 

  28. X.J. Su, F.Q. Xia, Y.D. Song, M.V. Basin, L. Zhao, \({\cal{L} }_{2}\)-\({\cal{L} }_{\infty }\) Output feedback controller design for fuzzy systems over switching parameters. IEEE Trans. Fuzzy Syst. 26(6), 3755–3769 (2018). https://doi.org/10.1109/TFUZZ.2018.2848652

    Article  Google Scholar 

  29. W.C. Sun, Y.Q. Yuan, Passivity based hierarchical multi-task tracking control for redundant manipulators with uncertainties. Automatica 155, 111159 (2023). https://doi.org/10.1016/j.automatica.2023.111159

    Article  MathSciNet  Google Scholar 

  30. B. Wang, H.B. Zhang, G. Wang, C.Y. Dang, Asynchronous \(H_\infty \) filtering for linear switched systems with average dwell time. Int. J. Syst. Sci. 47(12), 2783–2791 (2016). https://doi.org/10.1080/00207721.2015.1023758

    Article  MathSciNet  Google Scholar 

  31. J.L. Wang, J.L. Liang, C.T. Zhang, D.M. Fan, Robust dissipative filtering for impulsive switched positive systems described by the Fornasini–Marchesini second model. J. Frankl. Inst. 359(1), 123–144 (2022). https://doi.org/10.1016/j.jfranklin.2020.07.051

    Article  MathSciNet  Google Scholar 

  32. R.H. Wang, B.X. Xue, L.L. Hou, S.M. Fei, J.B. Zhao, Quasi-time-dependent \(L_2-L_\infty \) filtering of discrete-time switched systems with admissible edge-dependent average dwell time. Circuits Syst. Signal Process. 39(9), 4320–4338 (2020). https://doi.org/10.1007/s00034-020-01386-xv

    Article  Google Scholar 

  33. Z.Y. Wang, L.J. Gao, H.Y. Liu, Stability and stabilization of impulsive switched system with inappropriate impulsive switching signals under asynchronous switching. Nonlinear Anal. Hybrid Syst. 39, 100976 (2021). https://doi.org/10.1016/j.nahs.2020.100976

    Article  MathSciNet  Google Scholar 

  34. L.G. Wu, J. Lam, Weighted \(H_\infty \) filtering of switched systems with time-varying delay: average dwell time approach. Circuits Syst. Signal Process. 28(6), 1017–1036 (2009). https://doi.org/10.1007/s00034-009-9123-6

    Article  MathSciNet  Google Scholar 

  35. W.Q. Xie, H. Zhu, J. Cheng, S.M. Zhong, K.B. Shi, Finite-time asynchronous \(H_\infty \) resilient filtering for switched delayed neural networks with memory unideal measurements. Inf. Sci. 487, 156–175 (2019). https://doi.org/10.1016/j.ins.2019.03.019

    Article  MathSciNet  Google Scholar 

  36. S.Y. Xu, P.V. Dooren, R. Stefan, J. Lam, Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Trans. Autom. Control 47(7), 1122–1128 (2002). https://doi.org/10.1109/tac.2002.800651

    Article  MathSciNet  Google Scholar 

  37. L. Yang, C.X. Guan, Z.Y. Fei, Finite-time asynchronous filtering for switched linear systems with an event-triggered mechanism. J. Frankl. Inst. 356(10), 5503–5520 (2019). https://doi.org/10.1016/j.jfranklin.2019.03.019

    Article  MathSciNet  Google Scholar 

  38. B.Y. Zhang, W.X. Zheng, S.Y. Xu, Filtering of Markovian jump delay systems based on a new performance index. IEEE Trans. Circuits Syst. I Regul. Pap. 60(5), 1250–1263 (2013). https://doi.org/10.1109/TCSI.2013.2246213

    Article  MathSciNet  Google Scholar 

  39. L.X. Zhang, P. Shi, Stability, \(L_2\)-gain and asynchronous \(H_\infty \) control of discrete-time switched systems with average dwell-time. IEEE Trans. Autom. Control 54(9), 2192–2199 (2009). https://doi.org/10.1109/TAC.2009.2026841

    Article  ADS  Google Scholar 

  40. T.L. Zhang, F.Q. Deng, W.H. Zhang, Robust \(H_\infty \) filtering for nonlinear discrete-time stochastic systems. Automatica 123, 109343 (2021). https://doi.org/10.1016/j.automatica.2020.109343

    Article  MathSciNet  Google Scholar 

  41. T.X. Zhang, J.X. Li, W. Xu, X.D. Li, Stability and \(L_2\)-gain analysis for impulsive switched systems. Commun. Nonlinear Sci. Numer. Simul. 78, 104854 (2019). https://doi.org/10.1016/j.cnsns.2019.104854

    Article  MathSciNet  Google Scholar 

  42. Q.X. Zheng, S.Y. Xu, B.Z. Du, Asynchronous nonfragile guaranteed cost control for impulsive switched fuzzy systems with quantizations and its applications. IEEE Trans. Fuzzy Syst. 30(10), 4471–4483 (2022). https://doi.org/10.1109/TFUZZ.2022.3153144

    Article  Google Scholar 

  43. Q.X. Zheng, S.Y. Xu, B.Z. Du, Asynchronous nonfragile mixed \(H_\infty \) and \(L_2-L_\infty \) control of switched fuzzy systems with multiple state impulsive jumps. IEEE Trans. Fuzzy Syst. 31(6), 1966–1980 (2023). https://doi.org/10.1109/TFUZZ.2022.3216983

    Article  Google Scholar 

  44. Q.X. Zheng, S.Y. Xu, Z.Q. Zhang, Nonfragile quantized \(H_\infty \) filtering for discrete-time switched T-S fuzzy systems with local nonlinear models. IEEE Trans. Fuzzy Syst. 29(6), 1507–1517 (2021). https://doi.org/10.1109/TFUZZ.2020.2979675

    Article  Google Scholar 

  45. L. Zhou, X.Q. Xiao, New input-to-state stability condition for continuous-time switched nonlinear systems. Circuits Syst. Signal Process. 41(3), 1389–1405 (2022). https://doi.org/10.1007/s00034-021-01845-z

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Open Research Fund of Anhui Key Laboratory of Detection Technology and Energy Saving Devices (Grant no. JCKJ2022A05), the Natural Science Research Project of Colleges and Universities of Anhui Province (Grant no. 2023AH040123), and the National Natural Science Foundation of China (Grant nos. 61803001,61963010).

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Authors and Affiliations

  1. Anhui Key Laboratory of Detection Technology and Energy Saving Devices, Anhui Polytechnic University, Wuhu, People’s Republic of China

    Yufei Zhu, Xinya Mao & Qunxian Zheng

  2. School of Electrical Engineering, Anhui Polytechnic University, Wuhu, 241000, Anhui, People’s Republic of China

    Yufei Zhu, Xinya Mao & Qunxian Zheng

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Zhu, Y., Mao, X. & Zheng, Q. Asynchronous Hybrid \(H_\infty \) Filtering for Uncertain Impulsive Switched Systems. Circuits Syst Signal Process 43, 1392–1413 (2024). https://doi.org/10.1007/s00034-023-02533-w

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