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Observer-based mixed \(H_{\infty }\) and passive control for T-S fuzzy semi-Markovian jump systems with time-varying delay via sliding mode method

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Abstract

This article presents the subject of the Takagi–Sugeno fuzzy sliding mode approach for nonlinear semi-Markovian mode-dependent delay switching systems. In addition, the mixed \(H_{\infty }\)/passive performance was considered. The non-fragile observer is introduced to reconstruct variables, such that the error dynamics are obtained. By raising a novel fuzzy integral sliding surface function on the probability space, the new closed-loop sliding mode dynamic constitutes by observer and estimate systems satisfies both the mixed \(H_{\infty }\)/passive performance index and the stochastic stable as the new model-dependent Lyapunov–Krasovskii function is established. Moreover, sufficient conditions are carried out based on linear matrix inequality (LMI), which ensures the results of our work can be verified by the feasibility problem in terms of LMI. Then the sliding mode control is designed to make the system's trajectory reach the predefined sliding surface. Finally, four numerical examples are given to testify the availability and less conservatism of the theoretical method.

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References

  1. Sakthivel R, Divya H, Sakthivel R et al (2020) Robust hybrid control design for stochastic Markovian jump system via fault alarm approach. IEEE Trans Circuits Syst II Express Briefs 67(10):2004–2008

    Google Scholar 

  2. Zhang D, Du B, Jing Y et al (2022) Investigation on stability of positive singular Markovian jump systems with mode-dependent derivative-term coefficient. IEEE Trans Syst Man Cybern Syst 52(3):1385–1394

    Article  Google Scholar 

  3. Baranitha R, Mohajerpoor R, Rakkiyappan R (2021) Bilateral teleoperation of single-master multislave systems with semi-Markovian jump stochastic interval time-varying delayed communication channels. IEEE Trans Cybern 51(1):247–257

    Article  Google Scholar 

  4. Nie R, He S, Liu F et al (2021) Sliding mode controller design for conic-type nonlinear semi-Markovian jumping systems of time-delayed Chua’s circuit. IEEE Trans Syst Man Cybern Syst 51(4):2467–2475

    Article  Google Scholar 

  5. Zhuang G, Su S, Xia J et al (2021) HMM-based asynchronous filtering for fuzzy singular Markovian switching systems with retarded time-varying delays. IEEE Trans Cybern 51(3):1189–1203

    Article  Google Scholar 

  6. Ma YC, Kong CF (2020) Dissipative asynchronous T-S fuzzy control for singular semi-Markovian jump systems. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.3032398

    Article  Google Scholar 

  7. Guan C, Fei Z, Park P (2021) Modified looped functional for sampled-data control of T-S Fuzzy Markovian jump systems. IEEE Trans Fuzzy Syst 29(9):2543–2552

    Article  Google Scholar 

  8. Yan HC, Wang TT, Zhang H et al (2015) Event-triggered control for uncertain networked T-S fuzzy systems with time delay. Neurocomputing 157:273–279

    Article  Google Scholar 

  9. Li M, Chen X, Liu M et al (2022) Asynchronous adaptive fault-tolerant sliding-mode control for T-S fuzzy singular Markovian jump systems with uncertain transition rates. IEEE Trans Cybern 52(1):544–555

    Article  Google Scholar 

  10. Wang J, Ru T, Xia J et al (2021) Asynchronous event-triggered sliding mode control for semi-markov jump systems within a finite-time interval. IEEE Trans Circuits Syst I Regul Pap 68(1):458–468

    Article  Google Scholar 

  11. Kong CF, Ma YC, Liu DY (2019) Observer-based quantized sliding mode dissipative control for singular Semi-Markovian jump systems. Appl Math Comput 362:124539

    MATH  Google Scholar 

  12. Li R, Zhang X (2020) Adaptive sliding mode observer design for a class of T-S fuzzy descriptor fractional order systems. IEEE Trans Fuzzy Syst 28(9):1951–1960

    Article  Google Scholar 

  13. Jiang BP, Karimi H, Kao YG et al (2019) Takagi-Sugeno model-based sliding mode observer design for finite-time synthesis of Semi-Markovian jump systems. IEEE Trans Syst Man Cybern Syst 49:1505–1515

    Article  Google Scholar 

  14. Liu Z, Yu J (2020) Non-fragile observer-based adaptive control of uncertain nonlinear stochastic Markovian jump systems via sliding mode technique. Nonlinear Anal Hybrid Syst 38:100931

    Article  MATH  Google Scholar 

  15. Zhang L, Zhou Y, Qi W et al (2020) Non-fragile observer-based finite-time sliding mode control. Appl Math Comput 375:125069

    Google Scholar 

  16. Hua M, Zheng D, Deng F et al (2021) Filtering for nonhomogeneous markovian jump repeated scalar nonlinear systems with multiplicative noises and partially mode-dependent characterization. IEEE Trans Syst Man Cybern Syst 51(5):3180–3192

    Article  Google Scholar 

  17. Zheng Q, Zhang H, Ling Y et al (2018) Mixed and passive control for a class of nonlinear switched systems with average dwell time via hybrid control approach. J Franklin Inst 355(3):1156–1175

    Article  MATH  Google Scholar 

  18. Mathiyalagan K, Park JH, Sakthivel R et al (2014) Robust mixed and passive filtering for networked Markov jump systems with impulses. Signal Process 101:162–173

    Article  Google Scholar 

  19. Shi P, Zhang Y, Chadli M et al (2016) Mixed and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays. IEEE Trans Neural Netw Learn Syst 27(4):903–909

    Article  Google Scholar 

  20. Xia WF, Li YM, Chu YM et al (2019) Observer-based mixed passive and control for uncertain Markovian jump systems with time delays using quantized measurements. Nonlinear Anal Hybrid Syst 31:233–246

    Article  MATH  Google Scholar 

  21. Su L, Ye D (2018) Mixed and passive event-triggered reliable control for T-S fuzzy Markov jump systems. Neurocomputing 281:96–105

    Article  Google Scholar 

  22. Zhang S, Nie H (2022) Dwell-time-dependent asynchronous mixed and passive control for discrete-time switched systems. Nonlinear Anal Hybrid Syst 44:101140

    Article  MATH  Google Scholar 

  23. Wang X, Park JH, Yang H et al (2020) An improved fuzzy sampled-data control to stabilization of T-S fuzzy systems with state delays. IEEE Trans Cybern 50(7):3125–3135

    Article  Google Scholar 

  24. Lin Y, Zhuang G, Sun W et al (2021) Resilient dynamic output feedback controller design for USJSs with time-varying delays. Appl Math Comput 395:125875

    MATH  Google Scholar 

  25. Zhuang G, Sun W, Su S et al (2021) Asynchronous feedback control for delayed fuzzy degenerate jump systems under observer-based event-driven characteristic. IEEE Trans Fuzzy Syst 29(12):3754–3768

    Article  Google Scholar 

  26. Wang J, Ma S, Zhang C (2019) Finite-time control for T-S fuzzy descriptor semi-Markov jump systems via static output feedback. Fuzzy Sets Syst 365:60–80

    Article  MATH  Google Scholar 

  27. Li M, Huang Q (2019) Non-fragile passive control for Markovian jump systems with time-varying delays. Physica A 534:122332

    Article  MATH  Google Scholar 

  28. Qi WH, Park JH, Cheng J et al (2017) Robust stabilisation for non-linear time-delay semi-Markovian jump systems via sliding mode control. IET Control Theory Appl 11(10):1504–1513

    Article  Google Scholar 

  29. Tang PY, Ma YC (2019) Exponential stabilization and sampled-date control for uncertain T-S fuzzy systems with time-varying delay. J Franklin Inst 365:4859–4887

    Article  MATH  Google Scholar 

  30. Zhang Y, Ma Y, Fu L et al (2020) Finite-time non-fragile sampled-data control for uncertain T-S fuzzy system with time-varying delay and nonlinear perturbation subject to Markovian jump. ISA Trans 99:59–73

    Article  Google Scholar 

  31. Castanos F, Fridman L (2006) Analysis and design of integral sliding manifolds for systems with unmatched perturbations. IEEE Trans Autom Control 51(5):853–858

    Article  MATH  Google Scholar 

  32. Sakthivel R, Saravanakumar T, Ma YK et al (2017) Finite-time resilient reliable sampled-data control for fuzzy systems with randomly occurring uncertainties. Fuzzy Sets Syst 329:1–18

    Article  MATH  Google Scholar 

  33. Li ZC, Li M, Xu YL et al (2017) Finite-time stability and stabilization of semi-Markovian jump systems with time delay. Int J Robust Nonlinear Control 28(8):1–18

    Google Scholar 

  34. Gao HJ, Fei ZY, Lam J et al (2011) Further results on exponential estimates of Markovian jump systems with mode-dependent time-varying delays. IEEE Trans Autom Control 56(1):223–229

    Article  MATH  Google Scholar 

  35. Shu Z, Lam J, Xu SY (2006) Robust stabilization of Markovian delay systems with delay-dependent exponential estimates. Automatica 42(11):2001–2008

    Article  MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China No. 61273004, and the Natural Science Foundation of Hebei province No. F2021203061. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

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  1. School of Science, Yanshan University, Qinhuangdao, 066004, Hebei, People’s Republic of China

    Zhiqi Wei, Huan Li & Yuechao Ma

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  1. Zhiqi Wei
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  2. Huan Li
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Correspondence to Yuechao Ma.

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Wei, Z., Li, H. & Ma, Y. Observer-based mixed \(H_{\infty }\) and passive control for T-S fuzzy semi-Markovian jump systems with time-varying delay via sliding mode method. Int. J. Mach. Learn. & Cyber. 14, 253–268 (2023). https://doi.org/10.1007/s13042-022-01638-z

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