SpringerLink
Log in

Robust H∞ and Guaranteed Cost Filtering for T-S Fuzzy Systems with Multipath Quantizations

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

Abstract

This paper investigates the problems of robust H∞ and guaranteed cost filtering for discrete-time uncertain Takagi-Sugeno (T-S) fuzzy systems with multipath quantizations. The “multipath quantizations” mean that both the measurement output and estimated output of the uncertain T-S fuzzy systems are quantized by two different dynamic quantizers before they are transmitted. The unknown uncertain parameters are assumed to be norm bounded. Through applying the S-procedure and introducing some slack matrix variables, new sufficient conditions about the robust asymptotical stability with specific performance measures for quantized filtering error system have been developed via the fuzzy-basis-dependent Lyapunov function approach. The desired robust H∞ filter, robust guaranteed cost filter and dynamic quantizer parameters can be easily obtained by means of linear matrix inequalities (LMIs). Finally, a practical example about the mass-spring-damper mechanical system is given.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. X. Su, Y. Wen, P. Shi, and H. K. Lam, “Event-triggered fuzzy filtering for nonlinear dynamic systems via reduced-order approach,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 6, pp. 1215–1225, June 2019.

    Article  Google Scholar 

  2. J. Cheng and Y. Zhan, “Nonstationary l2 — l∞ filtering for Markov switching repeated scalar nonlinear systems with randomly occurring nonlinearities,” Applied Mathematics and Computation, vol. 365, 124714, 2020.

    Article  MATH  Google Scholar 

  3. C. K. Ahn, P. Shi, and M. V. Basin, “Two-dimensional peak-to-peak filtering for stochastic Fornasini-Marchesini systems,” IEEE Transactions on Automatic Control, vol. 63, no. 5, pp. 1472–1479, May 2018.

    Article  MATH  Google Scholar 

  4. X. Chang, Q. Liu, Y. Wang, and J. **ong, “Fuzzy peak-to-peak filtering for networked nonlinear systems with multipath data packet dropouts,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 3, pp. 436–446, March 2019.

    Article  Google Scholar 

  5. X. Liu, J. Zhuang, and Y. Li, “H∞ filtering for Markovian jump linear systems with uncertain transition probabilities,” International Journal of Control, Automation, and Systems, vol. 19, no. 7, pp. 2500–2510, July 2021.

    Article  Google Scholar 

  6. D. Zhang, Z. Xu, H. R. Karimi, and Q. Wang, “Distributed filtering for switched linear systems with sensor networks in presence of packet dropouts and quantization,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 64, no. 10, pp. 2783–2796, October 2017.

    Article  Google Scholar 

  7. Q. Zheng and H. Zhang, “H∞ filtering for a class of nonlinear switched systems with stable and unstable subsystems,” Signal Processing, vol. 141, pp. 240–248, 2017.

    Article  Google Scholar 

  8. H. Shen, Z. Huang, J. Cao, and J. H. Park, “Exponential H∞ filtering for continuous-time switched neural networks under persistent dwell-time switching regularity,” IEEE Transactions on Cybernetics, vol. 50, no. 6, pp. 2440–2449, June 2020.

    Article  Google Scholar 

  9. J. Yu, Y. Zhao, and Y. Wu, “Global robust output regulation control for cascaded nonlinear systems using the internal model principle,” International Journal of Control, vol. 87, no. 4, pp. 802–811, 2014.

    Article  MATH  Google Scholar 

  10. H. Ma, H. Li, R. Lu, and T. Huang, “Adaptive event-triggered control for a class of nonlinear systems with periodic disturbances,” Science China Information Sciences, vol. 63, no. 5, 150212, May 2020.

    Article  Google Scholar 

  11. J. Liu, X. Shen, A. M. Alcaide, Y. Yin, J. I. Leon, S. Vazquez, L. Wu, and L. G. Franquelo, “Sliding mode control of grid-connected neutral-point-clamped converters via high-gain observer,” IEEE Transactions on Industrial Electronics, vol. 69, no. 4, pp. 4010–4021, April 2022.

    Article  Google Scholar 

  12. Y. Li, X. Min, and S. Tong, “Observer-based fuzzy adaptive inverse optimal output feedback control for uncertain nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 6, pp. 1484–1495, June 2021.

    Article  Google Scholar 

  13. X. Zhao, X. Wang, L. Ma, and G. Zong, “Fuzzy-approximation-based asymptotic tracking control for a class of uncertain switched nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 28, no. 4, pp. 632–644, April 2020.

    Article  Google Scholar 

  14. J. Yu, P. Shi, X. Chen, and G. Cui, “Finite-time command filtered adaptive control for nonlinear systems via immersion and invariance,” Science China Information Sciences, vol. 64, no. 8, 192202, August 2021.

    Article  Google Scholar 

  15. T. Takagi and M. Sugeno, “Fuzzy identification of systems and its application to modeling and control,” IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-15, no. 1, pp. 116–132, January–February 1985.

    Article  MATH  Google Scholar 

  16. X. Su, F. **a, J. Liu, and L. Wu, “Event-triggered fuzzy control of nonlinear systems with its application to inverted pendulum systems,” Automatica, vol. 94, pp. 236–248, 2018.

    Article  MATH  Google Scholar 

  17. M. S. Aslam and X. Dai, “H∞ control for network T-S fuzzy systems under time varying delay for multi-area power systems,” International Journal of Control, Automation, and Systems, vol. 18, no. 11, pp. 2774–2787, November 2020.

    Article  Google Scholar 

  18. X. **e, D. Yue, and C. Peng, “Observer design of discrete-time fuzzy systems based on an alterable weights method,” IEEE Transactions on Cybernetics, vol. 50, no. 4, pp. 1430–1439, April 2020.

    Article  Google Scholar 

  19. R. Chaibi, H. E. Aiss, A. E. Hajjaji, and A. Hmamed, “Stability analysis and robust H∞ controller synthesis with derivatives of membership functions for T-S fuzzy systems with time-varying delay: Input-output stability approach,” International Journal of Control, Automation, and Systems, vol. 18, no. 7, pp. 1872–1884, July 2020.

    Article  Google Scholar 

  20. X. Li, B. Wang, L. Zhang, and X. Ma, “H∞ control with multiple packets compensation scheme for T-S fuzzy systems subject to cyber attacks,” International Journal of Control, Automation, and Systems, vol. 19, no. 1, pp. 230–240, January 2021.

    Article  Google Scholar 

  21. Y. Wang, X. **e, M. Chadli, S. **e, and Y. Peng, “Sliding mode control of fuzzy singularly perturbed descriptor systems,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 8, pp. 2349–2360, August 2021.

    Article  Google Scholar 

  22. Q. Zheng, S. Xu, and B. Du, “Quantized guaranteed cost output feedback control for nonlinear networked control systems and its applications,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 7, pp. 2402–2411, 2022.

    Article  Google Scholar 

  23. X. Chang, Z. Li, and J. H. Park, “Fuzzy generalized H2 filtering for nonlinear discrete-time systems with measurement quantization,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 12, pp. 2419–2430, December 2018.

    Article  Google Scholar 

  24. J. Dong and G. Yang, “H∞ filtering for continuous-time T-S fuzzy systems with partly immeasurable premise variables,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 1931–1940, August 2017.

    Article  Google Scholar 

  25. Z. Wu, S. Dong, P. Shi, D. Zhang, and T. Huang, “Reliable filter design of Takagi-Sugeno fuzzy switched systems with imprecise modes,” IEEE Transactions on Cybernetics, vol. 50, no. 5, pp. 1941–1951, May 2020.

    Article  Google Scholar 

  26. J. Qiu, H. Tian, Q. Lu, and H. Gao, “Nonsynchronized robust filtering design for continuous-time T-S fuzzy affine dynamic systems based on piecewise Lyapunov functions,” IEEE Transactions on Cybernetics, vol. 43, no. 6, pp. 1755–1766, December 2013.

    Article  Google Scholar 

  27. L. Y. Chung, C. H. Lien, K. W. Yu, and J. D. Chen, “Robust H∞ filtering for discrete switched systems with interval time-varying delay,” Signal Processing, vol. 94, no. 1, pp. 661–669, January 2014.

    Article  Google Scholar 

  28. M. Wang, J. Qiu, and G. Feng, “Finite frequency filtering design for uncertain discrete-time systems using past output measurements,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 65, no. 9, pp. 3005–3013, September 2018.

    Article  MATH  Google Scholar 

  29. Y. **e, J. Wen, and L. Peng, “Robust H∞ filtering for average dwell time switching systems via a non-monotonic function approach,” International Journal of Control, Automation, and Systems, vol. 17, no. 3, pp. 657–666, March 2019.

    Article  Google Scholar 

  30. X. Han and Y. Ma, “Sampled-data robust H∞ control for T-S fuzzy time-delay systems with state quantization,” International Journal of Control, Automation, and Systems, vol. 17, no. 1, pp. 46–56, January 2019.

    Article  Google Scholar 

  31. W. Qi, G. Zong, and H. R. Karimi, “Finite-time observer-based sliding mode control for quantized semi-Markov switching systems with application,” IEEE Transactions on Industrial Informatics, vol. 16, no. 2, pp. 1259–1271, February 2020.

    Article  Google Scholar 

  32. Z. Ning, L. Zhang, J. de Jesus Rubio, and X. Yin, “Asynchronous filtering for discrete-time fuzzy affine systems with variable quantization density,” IEEE Transactions on Cybernetics, vol. 47, no. 1, pp. 153–164, January 2017.

    Article  Google Scholar 

  33. C. J. Lee and M. T. Lim, “Fuzzy H∞ FIR filtering for T-S fuzzy systems with quantization and packet dropout,” International Journal of Control, Automation, and Systems, vol. 16, no. 3, pp. 961–971, May 2018.

    Article  Google Scholar 

  34. M. Hua, Y. Qian, F. Deng, J. Fei, P. Cheng, and H. Chen, “Filtering for discrete-time Takagi-Sugeno fuzzy nonhomogeneous Markov jump systems with quantization effects,” IEEE Transactions on Cybernetics, vol. 52, no. 2, pp. 982–995, February 2022.

    Article  Google Scholar 

  35. Q. Zheng, S. Xu, and Z. Zhang, “Nonfragile quantized H∞ filtering for discrete-time switched T-S fuzzy systems with local nonlinear models,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 6, pp. 1507–1517, June 2021.

    Article  Google Scholar 

  36. D. Liberzon, “Hybrid feedback stabilization of systems with quantized signals,” Automatica, vol. 39, no. 9, pp. 1543–1554, September 2003.

    Article  MATH  Google Scholar 

  37. J. H. Kim, S. J. Ahn, and S. J. Ahn, “Guaranteed cost and H∞ filtering for discrete time polytopic uncertain systems with time delay,” Journal of the Franklin Institute, vol. 342, no. 4, pp. 365–378, 2005.

    Article  MATH  Google Scholar 

  38. G. Zong, L. Hou, and Y. Wu, “Robust l2 — l∞ guaranteed cost filtering for uncertain discrete-time switched system with mode-dependent time-varying delays,” Circuits, Systems, and Signal Processing, vol. 30, pp. 17–33, 2011.

    Article  MATH  Google Scholar 

  39. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequality in Systems and Control Theory, SIAM, Philadelphia, PA, USA, 1994.

    Book  MATH  Google Scholar 

  40. S. Xu, P. V. Dooren, R. Stefan, and J. Lam, “Robust stability and stabilization for singular systems with state delay and parameter uncertainty,” IEEE Transactions on Automatic Control, vol. 47, no. 7, pp. 1122–1128, July 2002.

    Article  MATH  Google Scholar 

  41. Y. Wang, X. Xu, X. Li, L. Cheng, and H. Zhang, “Event-triggered H∞ filtering of continuous-time switched linear systems with overlapped mismatching intervals,” International Journal of Control, Automation, and Systems, vol. 19, no. 10, pp. 3368–3378, October 2021.

    Article  Google Scholar 

  42. H. Li, Y. Wu, M. Chen, and R. Lu, “Adaptive multigradient recursive reinforcement learning event-triggered tracking control for multi-agent systems,” IEEE Transactions on Neural Networks and Learning Systems, pp. 1–13, 2021. DOI: https://doi.org/10.1109/TNNLS.2021.3090570

  43. X. Su, Y. Wen, P. Shi, S. Wang, and W. Assawinchaichote, “Event-triggered fuzzy control for nonlinear systems via sliding mode approach,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 2, pp. 336–344, February 2021.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical Engineering, Anhui Polytechnic University, Wuhu, 241000, China

    Qunxian Zheng, Wei Shi, Ke Wu & Shengquan Jiang

Authors
  1. Qunxian Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ke Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shengquan Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qunxian Zheng.

Additional information

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

This work was supported by the National Natural Science Foundation of China (Grant no. 61803001), the National College Students’ Innovation and Entrepreneurship Training Program (Grant no. S202010363033), and the Support Program for Outstanding Youth Talents in Colleges and Universities of Anhui Province (Grant no. gxyqZD2022048).

Qunxian Zheng received his B.E. degree in biomedical engineering, an M.E. degree in biophysics, and a Ph.D. degree in circuits and systems from University of Electronic Science and Technology of China, Chengdu, in 2008, 2011, and 2016, respectively. He is currently working as an associate professor in Anhui Polytechnic University, Wuhu. His research interests include fuzzy control systems, switched systems, and networked control systems.

Wei Shi is currently working toward a B.E. degree in building electrical and intelligent in Anhui Polytechnic University, Wuhu.

Ke Wu is currently working toward a B.E. degree in building electrical and intelligent in Anhui Polytechnic University, Wuhu.

Shengquan Jiang is currently working toward a B.E. degree in building electrical and intelligent in Anhui Polytechnic University, Wuhu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zheng, Q., Shi, W., Wu, K. et al. Robust H∞ and Guaranteed Cost Filtering for T-S Fuzzy Systems with Multipath Quantizations. Int. J. Control Autom. Syst. 21, 671–683 (2023). https://doi.org/10.1007/s12555-021-0616-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-021-0616-9

Keywords

Search

Navigation