Quantized Finite-Time Non-fragile Filtering for Singular Markovian Jump Systems with Intermittent Measurements

  • Sakthivel RathinasamyEmail author
  • Sathishkumar Murugesan
  • Faris Alzahrani
  • Yong Ren


In this work, the finite-time non-fragile mixed \(H_\infty \) and passivity filter design problem for a class of discrete-time singular Markovian jump systems with time-varying delays, intermittent measurements and quantization is investigated. The measured output of the plant is quantized by a logarithmic mode-independent quantizer, and the time-varying transition probability matrix is described by a polytope. In this work, it is considered that the missing measurement phenomenon occurs during signal transmission from the plant to the filter, which is described by a stochastic variable that obeys the Bernoulli random binary distribution. Then, by constructing a proper Lyapunov–Krasovskii functional and using the linear matrix inequality (LMI) technique, sufficient conditions are obtained, which ensures that the augmented filtering system is stochastically finite-time boundedness with a prescribed mixed \(H_\infty \) and passive performance index. Moreover, the filter gains can be computed in terms of solution to a set of LMIs. Finally, two numerical examples are provided to demonstrate the effectiveness and potential of the proposed filter design technique.


Singular Markovian jump systems Filtering Intermittent measurements Time-varying delay 



The work of M. Sathishkumar was supported by the RGNF, UGC, New Delhi, India [Grant no. F1-17.1/2015-16/RGNF-2015-17-SC-TAM-18857/(SA-III/Website), dated: 09-01-2016].


  1. 1.
    J. Cheng, J.H. Park, H.R. Karimi, X. Zhao, Static output feedback control of nonhomogeneous Markovian jump systems with asynchronous time delays. Inf. Sci. 399, 219–238 (2017)CrossRefGoogle Scholar
  2. 2.
    J. Cheng, J.H. Park, Y. Liu, Z. Liu, L. Tang, Finite-time \(H_\infty \) fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions. Fuzzy Sets Syst. 314, 99–115 (2017)CrossRefzbMATHGoogle Scholar
  3. 3.
    Y. Ding, H. Liu, J. Cheng, \(H_\infty \) filtering for a class of discrete-time singular Markovian jump systems with time-varying delays. ISA Trans. 53, 1054–1060 (2014)CrossRefGoogle Scholar
  4. 4.
    Y. Ding, S. Zhong, S. Long, Asymptotic stability in probability of singular stochastic systems with Markovian switchings. Int. J. Robust Nonlinear Control 27, 4312–4322 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Z. Feng, J. Lam, Dissipative control and filtering of discrete-time singular systems. Int. J. Syst. Sci. 47, 2532–2542 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Y. Han, Y. Kao, C. Gao, Robust sliding mode control for uncertain discrete singular systems with time-varying delays and external disturbances. Automatica 75, 210–216 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    H.C. Hu, Y.C. Liu, Passivity-based control framework for task-space bilateral teleoperation with parametric uncertainty over unreliable networks. ISA Trans. 70, 187–199 (2017)CrossRefGoogle Scholar
  8. 8.
    Y. Kao, J. Xie, C. Wang, H.R. Karimi, Observer-based \(H_\infty \) sliding mode controller design for uncertain stochastic singular time-delay systems, Circuits. Syst. Signal Process. 35, 63–77 (2016)CrossRefzbMATHGoogle Scholar
  9. 9.
    O.M. Kwon, M.J. Park, Improved results on stability and stabilization criteria for uncertain linear systems with time-varying delays. Int. J. Comput. Math. 94, 2435–2457 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    H. Li, C. Wu, L. Wu, H.K. Lam, Y. Gao, Filtering of interval type-2 fuzzy systems with intermittent measurements. IEEE Trans. Cybern. 46, 668–678 (2016)CrossRefGoogle Scholar
  11. 11.
    S. Li, Y. Ma, Finite-time dissipative control for singular Markovian jump systems via quantizing approach. Nonlinear Ana. Hybrid Syst. 27, 323–340 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Y. Li, H.K. Lam, L. Zhang, Control design for interval type-2 polynomial fuzzy-model-based systems with time-varying delay. IET Control Theory Appl. 11, 2270–2278 (2017)MathSciNetCrossRefGoogle Scholar
  13. 13.
    J. Lin, S. Fei, J. Shen, Delay-dependent \(H_\infty \) filtering for discrete-time singular Markovian jump systems with time-varying delay and partially unknown transition probabilities. Signal Process. 91, 277–289 (2011)CrossRefzbMATHGoogle Scholar
  14. 14.
    D. Liu, G.H. Yang, Event-triggered non-fragile control for linear systems with actuator saturation and disturbances. Inf. Sci. 429, 1–11 (2018)MathSciNetCrossRefGoogle Scholar
  15. 15.
    G. Liu, Z. Qi, S. Xu, Z. Li, Z. Zhang, \(\alpha \)-Dissipativity filtering for singular Markovian jump systems with distributed delays. Signal Process. 134, 149–157 (2017)CrossRefGoogle Scholar
  16. 16.
    G. Liu, S. Xu, Y. Wei, Z. Qi, Z. Zhang, New insight into reachable set estimation for uncertain singular time-delay systems. Appl. Math. Comput. 320, 769–780 (2018)MathSciNetGoogle Scholar
  17. 17.
    H. Liu, P. Shi, H.R. Karimi, M. Chadli, Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay. Int. J. Syst. Sci. 47, 1433–1444 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Y. Ma, P. Yang, Y. Yan, Q. Zhang, Robust observer-based passive control for uncertain singular time-delay systems subject to actuator saturation. ISA Trans. 67, 9–18 (2017)CrossRefGoogle Scholar
  19. 19.
    H. Pan, W. Sun, H. Gao, X. Jing, Disturbance observer-based adaptive tracking control with actuator saturation and its application. IEEE Trans. Autom. Sci. Eng. 13, 868–875 (2016)CrossRefGoogle Scholar
  20. 20.
    H. Pan, W. Sun, H. Gao, J. Yu, Finite-time stabilization for vehicle active suspension systems with hard constraints. IEEE Trans. Intell. Transp. Syst. 16, 2663–2672 (2015)CrossRefGoogle Scholar
  21. 21.
    F.L. Qu, B. Hu, Z.H. Guan, Y.H. Wu, D.X. He, D.F. Zheng, Quantized stabilization of wireless networked control systems with packet losses. ISA Trans. 64, 92–97 (2016)CrossRefGoogle Scholar
  22. 22.
    R. Sakthivel, M. Sathishkumar, K. Mathiyalagan and S. Marshal Anthoni, Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties, Int. J. Adapt. Control Signal Process. 31 (2017) 39-53Google Scholar
  23. 23.
    M. Sathishkumar, R. Sakthivel, O.M. Kwon, B. Kaviarasan, Finite-time mixed \(H_\infty \) and passive filtering for Takagi-Sugeno fuzzy nonhomogeneous Markovian jump systems. Int. J. Syst. Sci. 48, 116–1427 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    M. Sathishkumar, R. Sakthivel, C. Wang, B. Kaviarasan and S. Marshal Anthoni, Non-fragile filtering for singular Markovian jump systems with missing measurements, Signal Process. 142 (2018) 125-136Google Scholar
  25. 25.
    B. Shen, H. Tan, Z. Wang, T. Huang, Quantized/saturated control for sampled-data systems under noisy sampling intervals: A confluent vandermonde matrix approach. IEEE Trans. Autom. Control 62, 4753–4759 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    H. Shen, S. Jiao, S. Huo, M. Chen, J. Li, B. Chen, On energy-to-peak filtering for semi-Markov jump singular systems with unideal measurements. Signal Process. 144, 127–133 (2018)CrossRefGoogle Scholar
  27. 27.
    H. Shen, L. Su, J.H. Park, Extended passive filtering for discrete-time singular Markov jump systems with time-varying delays. Signal Process. 128, 68–77 (2016)CrossRefGoogle Scholar
  28. 28.
    M. Shen, H. Zhang, J.H. Park, Observer-based quantized sliding mode \(H_\infty \) control of Markov jump systems. Nonlinear Dyn. 92, 415–427 (2018)CrossRefzbMATHGoogle Scholar
  29. 29.
    Y. Shi, Y. Tang, S. Li, Finite-time control for discrete time-varying systems with randomly occurring non-linearity and missing measurements. IET Control Theory Appl. 11, 838–845 (2017)MathSciNetCrossRefGoogle Scholar
  30. 30.
    J. Tao, R. Lu, P. Shi, H. Su, Z.G. Wu, Dissipativity-based reliable control for fuzzy Markov jump systems with actuator faults. IEEE Trans. Cybern. 47, 2377–2388 (2017)CrossRefGoogle Scholar
  31. 31.
    G. Wang, H. Bo, Q. Zhang, \(H_\infty \) filtering for time-delayed singular Markovian jump systems with time-varying switching: A quantized method. Signal Process. 109, 14–24 (2015)CrossRefGoogle Scholar
  32. 32.
    J. Wang, S. Ma, C. Zhang, Finite-time stabilization for nonlinear discrete-time singular Markov jump systems with piecewise constant transition probabilities subject to average dwell time. J. Franklin Inst. 354, 2102–2124 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Z. Wang, H. Dong, B. Shen, H. Gao, Finite-horizon \(H_\infty \) filtering with missing measurements and quantization effects. IEEE Trans. Autom. Control 58, 1707–1718 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    G. Wei, Z. Wang, B. Shen, M. Li, Probability-dependent gain-scheduled filtering for stochastic systems with missing measurements, IEEE Trans. Circuits Syst. II: Express Br. 58, 753–757 (2011)CrossRefGoogle Scholar
  35. 35.
    C. Wu, H. Li, H.K. Lam, H.R. Karimi, Fault detection for nonlinear networked systems based on quantization and dropout compensation: An interval type-2 fuzzy-model method. Neurocomputing 191, 409–420 (2016)CrossRefGoogle Scholar
  36. 36.
    Z.G. Wu, P. Shi, Z. Shu, H. Su, R. Lu, Passivity-based asynchronous control for Markov jump systems. IEEE Trans. Autom. Control 62, 2020–2025 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    D. Yao, R. Lu, Y. Xu, L. Wang, Robust \(H_\infty \) filtering for Markov jump systems with mode-dependent quantized output and partly unknown transition probabilities. Signal Process. 137, 328–338 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Sakthivel Rathinasamy
    • 1
    Email author
  • Sathishkumar Murugesan
    • 2
  • Faris Alzahrani
    • 3
  • Yong Ren
    • 4
  1. 1.Department of Applied MathematicsBharathiar UniversityCoimbatoreIndia
  2. 2.Department of MathematicsAnna University Regional CampusCoimbatoreIndia
  3. 3.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  4. 4.Department of MathematicsAnhui Normal UniversityWuhuChina

Personalised recommendations