Skip to main content
SpringerLink
Log in

Mode-dependent H∞ Filtering for Time-varying Delays Neutral Jump Systems Based on FWM Technique

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper is concerned with the problem of mode dependent H∞ filter for uncertainty Markovian jump system with neutral delay and retarded time-varying delay. By using free weight matrix (FWM) technique, the stability conditions of delay dependent are obtained under the framework of Lyapunov stability theory. Based on those result, the delay dependent conditions for full order and mode dependent Markovian jump linear filters are gained, which are expressed by Linear matrix inequalities (LMIs). Finally, a numerical example and a PEEC practical example are employed to prove the validity of the results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Xu, J. Lam, and X. Mao, “Delay-dependent H∞ control and filtering for uncertain Markovian jump systems with time-varying delays,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 54, no. 9, pp. 2070–2077, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  2. B. Zhang, W. X. Zheng, and S. Xu, “On robust H∞ filtering of uncertain Markovian jump time-delay systems,” International Journal of Adaptive Control and Signal Processing, vol. 26, no. 2, pp. 138–157, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Cheng, J. H. Park, J. Cao, and W. Qi, “A hidden mode observation approach to finite-time SOFC of Markovian switching systems with quantization,” Nonlinear Dynamics, vol. 100, pp. 509–521, 2020.

    Article  MATH  Google Scholar 

  4. G. Zhuang, Q. Ma, B. Zhang, S. Xu, and J. Xia, “Admissibility and stabilization of stochastic singular Markovian jump systems with time-delays,” System & Control Letters, vol. 114, pp. 1–10, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  5. Y. Zhu, X. Song, M. Wang, and J. Lu, “Finite-time asynchronous H∞ filtering design of Markovian jump systems with randomly occurred quantization,” International Journal of Control, Automation, and Systems, vol. 18, no. 2, pp. 450–461, 2020.

    Article  Google Scholar 

  6. R. Kavikumar, R. Sakthivel, O. M. Kwon, and B. Kaviarasan, “Reliable non-fragile memory state feedback controller design for fuzzy Markov jump systems,” Nonlinear Analysis: Hybrid Systems, vol. 35, p. 100828, 2020.

    MathSciNet  MATH  Google Scholar 

  7. G. Zhuang, J. Xia, J. Feng, W. Sun, and B. Zhang, “Admissibilization for implicit jump systems with mixed retarded delays based on reciprocally convex integral inequality and Barbalat’s lemma,” IEEE Transactions on Systems, Man, and Cybernetics, 2020. DOI: https://doi.org/10.1109/TSMC.2020.2964057

  8. Z. Wu, P. Shi, Z. Shu, H. Su, and R. Lu, “Passivity-based asynchronous control for Markov jump systems,” IEEE Transactions on Automatic Control, vol. 62, no. 4, pp. 2020–2025, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Zhu, Q. L. Han, and C. Zhang, “L1-stochastic stability and L1-gain performance of positive Markov jump linear systems with time-delays: necessary and sufficient conditions,” IEEE Transactions on Automatic Control, vol. 62, no. 7, pp. 3634–3639, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  10. H. Ren, G. Zong, and H. R. Karimi, “Asynchronous finite-time filtering of Markov jump nonlinear systems and its applications,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019. DOI: https://doi.org/10.1109/TSMC.2019.2899733

  11. H. Shen, Y. Wang, J. Xia, J. H. Park, and Z. Wang, “Fault-tolerant leader-following consensus for multi-agent systems subject to semi-Markov switching topologies: An event-triggered control scheme,” Nonlinear Analysis: Hybrid Systems, vol. 34, pp. 92–107, 2019.

    MathSciNet  MATH  Google Scholar 

  12. H. Shang, W. H. Qi, and G. D. Zong, “Asynchronous H∞ control for positive discrete-time markovian jump systems,” International Journal of Control, Automation, and Systems, vol. 18, no. 2, pp. 431–438, 2020.

    Article  Google Scholar 

  13. H. Gao, J. Xia, and G. Zhuang, “Robust finite-time extended dissipative control for a class of uncertain switched delay systems,” International Journal of Control, Automation and Systems, vol. 16, no. 3, pp. 1459–1468, 2018.

    Article  Google Scholar 

  14. J. Xia, G. Chen, J. H. Park, Hao Shen, and G. Zhuang, “Dissipativity-based sampled-data control for fuzzy switched Markovian jump systems,” IEEE Transactions on Fuzzy Systesms, 2020. DOI: https://doi.org/10.1109/TFUZZ.2020.2970856

  15. J. Cheng, J. H. Park, X. Zhao, H. R. Karimi, and J. Cao, “Quantized nonstationary filtering of network-based Markov switching RSNSs: a multiple hierarchical structure strategy,” IEEE Transactions on Automatic Control, vol. 65, no. 11, pp. 4816–4823, 2020.

    Article  MathSciNet  MATH  Google Scholar 

  16. Z. H. Xu, H. J. Ni, H. R. Karimi, and D. Zhang, “A Markovian jump system approach to consensus of heterogeneous multi-agent systems with partially unknown and uncertain attack strategies,” International Journal or Robust and Nonlinear Control, vol. 30, pp. 3039–3053, 2020.

    Article  MathSciNet  Google Scholar 

  17. J. Zhang, M. Li, and Raissi, T, “Reliable actuator fault control of positive switched systems with double switchings,” Asian Journal of Contral, 2020. DOI: https://doi.org/10.1002/asjc.2338

  18. J. Zhang and T. Raissi, “Saturation control of switched nonlinear systems,” Nonlinear Analysis: Hybird Systems, vol. 32, pp. 320–336, 2019.

    MathSciNet  MATH  Google Scholar 

  19. L. Liu, J. Zhang, Y. Shao, and X. Deng, “Event-triggered control of positive switched systems based on linear programming,” IET Contral Theory and Applications, vol. 14, no. 1, pp. 145–155, 2019.

    Article  Google Scholar 

  20. D. Zhao, H. R. Karimi, R. Sakthivel, and Y. Li, “Nonfragile fault-tolerant control for nonlinear Markovian jump systems with intermittent actuator fault,” Nonlinear Analysis: Hybrid Systems, vol. 32, pp. 337–350, 2019.

    MathSciNet  MATH  Google Scholar 

  21. B. Jiang, H. R. Karimi, S. Yang, C. C. Gao, and Y. Kao, “Observer-based adaptive sliding mode control for nonlinear stochastic Markov jump systems via T-S fuzzy modeling: Applications to robot arm model,” IEEE Transactions on Industrial Electronics, vol. 68, no. 1, pp. 466–477, 2020.

    Article  Google Scholar 

  22. J. Cheng, J. H. Park, H. R. Karimi, and X. Zhao, “Static output feedback control of nonhomogeneous Markovian jump systems with asynchronous time delays,” Information Sciences, vol. 399, pp. 219–238, 2017.

    Article  MATH  Google Scholar 

  23. D. Zhang, Y. P. Shen, S. Q. Zhou, X. W. Dong, and L. Yu, “Distributed secure platoon control of connected vehicles subject to DOS attack: theory and application,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2020. DOI: https://doi.org/10.1109/TSMC.2020.2968606

  24. G. Chen, J. Xia, and G. Zhuang, “Delay-dependent stability and dissipativity analysis of generalized neural networks with Markovian jump parameters and two delay components,” Journal of the Franklin Institute, vol. 353, no. 9, pp. 2137–2158, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  25. Q. Zhou, S. Zhao, H. Li, R. Lu, and C. Wu, “Adaptive neural network tracking control for robotic manipulators with dead-zone,” IEEE Transactions on Neural Networks and Learning Systems, vol. 30, no. 12, pp. 3611–3620, 2019.

    Article  MathSciNet  Google Scholar 

  26. S. Xu, and J. Lam, “A survey of linear matrix inequality techniques in stability analysis of delay systems,” International Journal of Systems Sciences, vol. 39, no. 12, pp. 1095–1113, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  27. X. Zhao, and Q. Zeng, “Stabilization of jump linear systems with mode-dependent time varying delays,” Optimal Control Application and Methods, vol. 32, no. 2, pp. 139152, 2011.

    Article  MathSciNet  Google Scholar 

  28. Y. Chen, and W. Zheng, “Stability analysis and control for switched stochastic delayed systems,” International Journal of Robust and Nonlinear Control, vol. 26, no. 2, pp. 303–328, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  29. Y. Liu, J. H. Park, and F. Fang, “Global exponential stability of delayed neural networks based on a new integral inequality,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 11, pp. 2318–2325, 2019.

    Article  Google Scholar 

  30. D. Zhang, Z. H. Xu, G. Feng, and H. Y. Li, “Asynchronous resilient output consensus of switched heterogeneous linear multivehicle systems with communication delay,” IEEE/ASME Transactions on Mechatronics, vol. 24, no. 6, pp: 2627–2640, 2019.

    Article  Google Scholar 

  31. J. Zhou, Y. Liu, J. H. Park, Q. Kong, and Z. Wang, “Fault-tolerant anti-synchronization control for chaotic switched neural networks with time delay and reaction diffusion,” Discrete & Continuous Dynamical Systems-S, vol. 14, no. 4, pp. 1569–1589, 2021.

    Article  MathSciNet  Google Scholar 

  32. G. Liu, S. Xu, J. H. Park, and G. Zhuang, “Reliable exponential H∞ filtering for singular Markovian jump systems with time-varying delays and sensor failures,” International Journal of Robust and Nonlinear Control, vol. 28, no. 14, pp. 4230–4245, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  33. R. Sakthivel, M. Joby, K. Mathiyalagan, and S. Santra, “Mixed H∞ and passive control for singular Markovian jump systems with time delays,” Journal of the Franklin Institute, vol. 352, no. 10, pp. 4446–4466, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  34. G. Zhuang, S. Xu, B. Zhang, H. Xu, and Y. Chu, “Robust H∞ deconvolution filtering for uncertain singular Markovian jump systems with time-varying delays,” International Journal of Robust and Nonlinear Control, vol. 26, no. 12, pp. 2564–2585, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  35. B. Zhang, S. Zhou, and S. Xu, “Delay-dependent H∞ controller design for linear neutral systems with discrete and distributed delays,” International Journal of Systems Science, vol. 38, no. 8, pp. 611–621, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  36. J. H. Park, O. M. Kwon, and S. M. Lee, “LMI optimization on stability for delay neural networks of neutral type,” Applied Mathematics and Computation, vol. 196, no. 1, pp. 236–244, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  37. S. Xu, J. Lam, and C. Yang, “H∞ and positive-real control for linear neutral delay systems,” IEEE Transactions on Automatic Control, vol. 46, no. 8, pp. 1321–1326, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  38. D. Yue and Q. Han, “A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model,” IEEE Transactions on Circults and Systems II: Express Briefs, vol. 51, no. 12, pp. 13211022, 2004.

    Google Scholar 

  39. Q. Han, “On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty,” Automatica, vol. 40, no. 6, pp. 1087–1092, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  40. J. H. Park, O. M. Kwon, and S. Won, “LMI approach to robust H∞ filtering for neutral delay differential systems,” Applied Mathematics and Computation, vol. 150, no. 1, pp. 235–244, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  41. M. Wu, Y. He, and J. She, “New delay-dependent stability criteria and stabilizing method for neutral systems,” IEEE Transactions on Automatic Control, vol. 49, no. 12, pp. 2266–2271, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  42. G. Chen, and Y. Shen, “Robust H∞ filter design for neutral stochastic uncertain systems with time-varying delay,” Journal of Mathematical Analysis and Applications, vol. 353, no. 1, pp. 196–204, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  43. Y. Chen, W. Qian, and S. Fei, “Improved robust stability conditions for uncertain neutral systems with discrete and distributed delays,” Journal of the Franklin Institute, vol. 352, no. 7, pp. 2634–2645, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  44. B. Zhang, S. Xu, Q. Ma, and Z. Zhang, “Output-feedback stabilization of singular LPV systems subject to inexact scheduling parameters,” Automatica, vol. 104, pp. 1–7, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  45. P. Balasubramaniam, A. Manivannan, and R. Rakkiyappan, “Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters,” Applied Mathematics and Computation, vol. 216, no. 11, pp. 3396–3407, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  46. L. Xiong, J. Tian, and X. Liu, “Stability analysis for neutral Markovian jump systems with partially unknown transition probabilities,” Journal of the Franklin Institute, vol. 349, pp. 2193–2214, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  47. G. Zhuang, S. Xu, J. W. Xia, Q. Ma, and Z. Q. Zhang, “Non-fragile delay feedback control for neutral stochastic Markovian jump systems with time-varying delays,” Applied Mathematics and Computation, vol. 355, pp. 21–32, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  48. Y. Su, M. Chen, B. Chen, and C. Lin, “Fuzzy H∞ filter design for nonlinear discrete-time systems with time-varying delays,” International Journal of Innovative Computing, Information and Control, vol. 6, no. 10, pp. 4335–4346, 2010.

    Google Scholar 

  49. Y. Liu, F. Fang, and J. H. Park, “Decentralized dissipative filtering for delayed nonlinear interconnected systems based on T-S fuzzy model,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 4, pp. 790–801, 2019.

    Article  Google Scholar 

  50. J. Xiong, X. Chang, and X. Yi, “Design of robust nonfragile fault detection filter for uncertain dynamic systems with quantization,” Applied Mathematics and Computation, vol. 338, pp. 774–788, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  51. W. Sun, Y. Wu, and Z. Sun, “Command filter-based finite-time adaptive fuzzy control for uncertain nonlinear systems with prescribed performance,” IEEE Transactions on Fuzzy Systems, vol. 28, no. 12, pp. 3161–3170, 2020.

    Article  Google Scholar 

  52. J. Xia, B. Li, S-F. Su, W. Sun, and H. Shen, “Finite-time command filtered event-triggered adaptive fuzzy tracking control for stochastic nonlinear systems,” IEEE Transactions on Fuzzy Systems, 2020. DOI: https://doi.org/10.1109/TFUZZ.2020.2985638

  53. J. Xiong and J. Lam, “Fixed-order robust H∞ filter design for Markovian jump systems with uncertain switching probabilities,” IEEE Transactions on Signal Processing, vol. 54, no. 4, pp. 1421–1430, 2006.

    Article  MATH  Google Scholar 

  54. X. H. Chang and G. H. Yang, “Nonfragile H∞ filtering of continuous-time fuzzy systems,” IEEE Transactions on Signal Processing, vol. 59, no. 4, pp. 1528–1538, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  55. W. Sun, S. Su, Y. Wu, and J. Xia, “A novel adaptive fuzzy control for output constrained stochastic non-strict feedback nonlinear systems,” IEEE Transactions on Fuzzy Systems, 2020. DOI: https://doi.org/10.1109/TFUZZ.2020.2969909

  56. X. H. Chang and G. H. Yang, “Nonfragile H∞ filter design for T-S fuzzy systems in standard form,” IEEE Transactions on Industrial Electronics, vol. 61, no. 7, pp. 3448–3458, 2014.

    Article  Google Scholar 

  57. Z. Wu, H. Su, and J. Chu, “H filtering for singular Markovian jump systems with time delay,” International Journal of Robust and Nonlinear Control, vol. 20, pp. 939–957, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  58. B. Zhang, W. Zheng, and S. Xu, “Filtering of Markovian jump delay systems based on a new performance index,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 54, no. 9, pp. 1250–1263, 2013.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252000, China

    Guowei Zhao, Guangming Zhuang, Jianwei Xia, Wei Sun & Junsheng Zhao

  2. School of Mathematics and Statistics, Hubei University of Arts and Science, XiangYang, 441002, China

    Minsong Zhang

Authors
  1. Guowei Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guangming Zhuang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianwei Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Junsheng Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Minsong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guangming Zhuang.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors would like to thank the Editors and the Referees for their valuable comments and suggestions, which helped to greatly improve the work. This work was partially supported by the National Natural Science Foundation of China under Grants 61773191, 61973148; Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions under Grant 2019KJI010; the Natural Science Foundation of Shandong Province for Outstanding Young Talents in Provincial Universities under Grant ZR2016JL025; the Natural Science Foundation of Shandong Province for Key Projects under Grant ZR2020KA010;Undergraduate Education Reform Project of higher Education in Shandong Province under Grant M2018X047; Liaocheng University Education Reform Project Foundation under Grants G201811, 26322170267.

Guowei Zhao received his B.Sc. degree in mathematics and applied mathematics from Liaocheng University, Liaocheng, China, in 2018. He is currently a graduate student of the School of Mathematical Sciences, Liaocheng University. His current research interests include neutral systems, Markov jump systems, time-delay systems, robust control and filtering.

Guangming Zhuang received his M.Sc. degree in probability and mathematical statistics from Southwest University, Chongqing, China, in 2007 and Ph.D. degree in control theory and control engineering from Nanjing University of Science and Technology in 2016. Since July, 2007, he has been with the School of Mathematical Sciences, Liaocheng University, Liaocheng, China. He is currently an Associate Professor of the School of Mathematical Sciences, Liaocheng University. Dr. Zhuang was a recipient of the Natural Science Foundation of Shandong Province for Outstanding Young Talents in Provincial Universities in the year 2016. He is the Leader of Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions. His research interests include singular systems, stochastic systems control and filtering.

Jianwei Xia received his Ph.D. degree in automatic control from Nanjing University of Science and Technology in 2007. From 2010 to 2012, he worked as a Postdoctoral Research Associate in the School of Automation, Southeast University, Nanjing, China. From 2013 to 2014, he worked as a Postdoctoral Research Associate in the Department of Electrical Engineering, Yeungnam University, Kyongsan, Korea. He is a Professor of the School of Mathematical Sciences, Liaocheng University. His research topics are robust control, stochastic systems and neural networks.

Wei Sun received his M.Sc. degree in operation research and control theory from Qufu Normal University in 2011 and his Ph.D. degree from the School of Automation, Southeast University in 2014. He was a Postdoctoral Researcher at Department of Electrical Engineering, National Taiwan University of Science and Technology. He is currently an Associate Professor of the School of Mathematical Sciences, Liaocheng University. His research interests cover nonlinear system control, adaptive theory, fuzzy control, and robotics.

Junsheng Zhao received his M.Sc. degree from the School of Mathematics, Qufu Normal University, China, in 2006 and his Ph.D. degree from the School of Automation, Southeast University, China, in 2014. He is currently an Associate Professor of the School of Mathematical Sciences, Liaocheng University. His main interests include learning dynamics in the dynamic systems, nonlinear system and neural networks.

Minsong Zhang received her Ph.D. degree from the School of Automation, Nanjing University of Science and Technology, China, in 2015. She has been with the School of Mathematics and Statistics, Hubei University of Arts and Science, XiangYang, Hubei, China. Her research interests include time-delay systems, robust control, and nonlinear systems.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, G., Zhuang, G., Xia, J. et al. Mode-dependent H∞ Filtering for Time-varying Delays Neutral Jump Systems Based on FWM Technique. Int. J. Control Autom. Syst. 19, 2092–2104 (2021). https://doi.org/10.1007/s12555-020-0362-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-020-0362-4

Keywords

Search

Navigation