Skip to main content
SpringerLink
Log in

H\(_{\infty }\) filter design for nonlinear systems with interval time-varying delay via T-S fuzzy models

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

This paper addresses the H\(_{\infty }\) filters design problem for delayed nonlinear systems subject to \({\mathscr{L}}_{2}-\)norm disturbances via Takagi-Sugeno (T-S) fuzzy approach with interval time-varying delay. An appropriate Lyapunov-Krasovskii functional (LKF) is established in the framework of augmented system. Then, on the basis of the free-weighting matrix technique and convex method, some improved integral inequality are employed and combined with a decoupling approach without ignoring any useful terms. Therefore, less conservative delay dependent conditions are obtained in terms of linear matrix inequality (LMIs), wish can be solved by using the Matlab LMI toolbox, to achieve the desired H\(_{\infty }\) performance. Finally, three numerical examples are given to demonstrate the advantages and the effectiveness of the obtained results, compared with some previous method in the literature.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Data Availability

The data that supports the findings of this study are available in “Numerical Examples” of this article.

References

  1. Ahmida F, Tissir EH (2014) Robust H\(_{\infty }\) control of switched T-S fuzzy systems with time varying delay. Appl Math Sci 8 (164):8179–8197

    Google Scholar 

  2. Ahmida F, Tissir EH (2015) A new approach to H\(_{\infty }\) filtering for switched T-S fuzzy systems with interval time varying delays and parameter uncertainties. British J Mathematics Computer Sci 6(3):215–232

    Article  Google Scholar 

  3. Anderson BDO, Moore JB (1979) Optimal filtering, Engle-wood, NJ: prentice-hall

  4. Basin M, Alvarez DC (2011) Delay-dependent stability for vector nonlinear stochastic systems with multiple delays. Int J Innovative Computing, Information Control 7(4):1565–1576

    Google Scholar 

  5. Belamfedel AS, Tissir EH, Chaibi N (2019) Small-gain theorem and finite-frequency analysis of TCP/AQM system with time varying delay. IET Control Theory Appli 13(13):1971–1982

    Article  MathSciNet  Google Scholar 

  6. Boukili B, Zoulagh T, Hmamed A, Tadeo F (2016) Robust H\(_{\infty }\) filtering for 2D systems with perturbation stochastic, 5th Conf. Systems and Control, Marrakesh, Morocco, pp 326–331

  7. Chaibi R, El Aiss H, El Hajjaji A, Hmamed A (2020) Stability analysis and robust H\(_{\infty }\) controller synthesis with derivatives of membership functions for T-S fuzzy systems with time-varying delay: input-output stability approach. Int J Control, Automation Syst 18:1–13

    Google Scholar 

  8. Cheng J, Shan Y, Cao J, Park JH (2021) Nonstationary control for T-S fuzzy Markovian switching systems with variable quantization density. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2020.2974440

  9. Cheng J, Park JH, Cao J, Qi W A hidden mode observation approach to finite-time SOFC of Markovian switching systems with quantization, Nonlinear Dynamics. https://doi.org/10.1007/s11071-020-05501-0

  10. El Aiss H, Hmamed A, El Hajjaji A (2017) Improved stability and H\(_{\infty }\) performance criteria for linear systems with interval time-varying delays via three terms approximation. Int J Syst Sci 48(16):3450–3458

    Article  MathSciNet  MATH  Google Scholar 

  11. El Aiss H, Zoulagh T, Hmamed A, El Hajjaji A, Bosche J (2018) Further results on H\(_{\infty }\) filtering design for continuous time-systems with time-varying delay systems: three term approximation approach, 7th Int. Conf. on Systems and Control, Valencia, Spain, pp 313–320

  12. El Aiss H, Zoulagh T, Hmamed A, El Hajjaji A (2019) An input-output approach to H\(_{\infty }\) reduced filter design for polytopic time-varying delay systems. Int J Syst Sci 50 (1):35–49

    Article  MathSciNet  MATH  Google Scholar 

  13. El Fezazi N (2019) An observer-based controller for congestion control in data networks. J Control Automation Electrical Syst 30(5):645–656

    Article  Google Scholar 

  14. El Fezazi N, El Haoussi F, Tissir EH, Bender FA, Alvarez T (2019) Multiclass AQM on a TCP/IP router: a control theory approach. Int J Robust Nonlinear Control 29(6):1719–1733

    Article  MathSciNet  MATH  Google Scholar 

  15. El Fezazi N, Tissir EH, El Haoussi F, Bender FA, Husain AR (2019) Controller synthesis for steer-by-wire system performance in vehicle. Iranian J Sci Technology, Trans Electrical Engineering 43(4):813–825

    Article  Google Scholar 

  16. El-Amrani A, Boukili B, El Hajjaji A, Hmamed A (2018) Robust H\(_{\infty }\) filter for uncertain continuous-time systems with finite frequency ranges, 26th Mediterranean Conf. on Control and Automation, Zadar, Croatia, pp 807–812

  17. El-Amrani A, Boukili B, Hmamed A, El Hajjaji A, Boumhidi I (2018) Robust H\(_{\infty }\) filtering for 2D continuous systems with finite frequency specifications. Int J Syst Sci 49(1):43–57

    Article  MathSciNet  MATH  Google Scholar 

  18. El-Kasri C, Hmamed A, Tissir EH, Tadeo F (2013) Robust H\(_{\infty }\) filtering for uncertain two-dimensional continuous systems with time-varying delays. Multidimensional Syst Signal Processing 24:685–706

    Article  MathSciNet  MATH  Google Scholar 

  19. Farkous R, Tissir EH (2016) H\(_{\infty }\) finite time state and sensor faults estimation for T-S fuzzy systems using descriptor technique, 5th IEEE Int. Conf. on Systems and Control, Marrakesh, Morocco, pp 288–293

  20. Gao H, Lam J, Shi P, Wang C (2005) Parameter-dependent filter design with guaranteed H\(_{\infty }\) performance. IEE Proceedings-Control Theory Appli 152(5):531–537

    Article  Google Scholar 

  21. Han X, Ma Y (2019) Sampled-data robust H\(_{\infty }\) control for T-S fuzzy time-delay systems with state quantization. Int J Control, Automation Syst 17(1):46–56

    Article  Google Scholar 

  22. Huang H, Ding S, Zhao L, Huang H, Chen L, Gao H, Ahmed SH (2020) Real-time fault-detection for IIoT facilities using GBRBM-based DNN. IEEE Internet Things J 7(7):5713–5722. https://doi.org/10.1109/JIOT.2019.2948396

    Article  Google Scholar 

  23. Huang S-J, He X-Q, Zhang N-N (2010) New results on H\(_{\infty }\) filter design for nonlinear systems with time delay via T-S fuzzy models. IEEE Trans Fuzzy Syst 19(1):193–199

    Article  Google Scholar 

  24. Hussain W, Merigó JM, Raza MR, Gao H (2022) A new QoS prediction model using hybrid IOWA-ANFIS with fuzzy C-means, subtractive clustering and grid partitioning. Inf Sci 584:280–300. https://doi.org/10.1016/j.ins.2021.10.054

    Article  Google Scholar 

  25. Idrissi S, Tissir EH, Boumhidi I (2017) Delay-dependent robust stabilization for uncertain T-S fuzzy systems with additive time varying delays. Int J Automation Smart Technology 7(2):71–78

    Article  Google Scholar 

  26. Idrissi S, Tissir EH, Boumhidi I, Chaibi N (2013) New delay dependent robust stability criteria for T-S fuzzy systems with constant delay. Int J Control, Automation Syst 11(5):885–892

    Article  Google Scholar 

  27. Idrissi S, Tissir EH, Boumhidi I, Chaibi N (2014) Robust H\(_{\infty }\) control for uncertain T-S fuzzy systems via delay partitioning approach. Int J Ecology Development 28(2):1–13

    Google Scholar 

  28. Idrissi S, Tissir EH, Boumhidi I, El Fezazi N (2020) Stability analysis and H\(_{\infty }\) performance for nonlinear T-S fuzzy systems with time-varying delay, 6th IEEE Int. Conf. on Optimization and Applications, Beni Mellal, Morocco, 1-4

  29. Kalman RE (1960) A new approach to linear filtering and prediction problems. Trans ASME J Basic Engineering 82:35–45

    Article  MathSciNet  Google Scholar 

  30. Kim J-H (2010) Delay-dependent approach to robust H\(_{\infty }\) filtering for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties. Int J Control, Automation Syst 8(3):655–661

    Article  Google Scholar 

  31. Lamrabet O, El Fezazi N, El Haoussi F, Tissir EH, Alvarez T (2020) Congestion control in TCP/IP routers based on sampled-data systems theory. J Control, Automation Electrical Syst 31:588–596

    Article  Google Scholar 

  32. Lamrabet O, Tissir EH, El Fezazi N, El Haoussi F (2020) Input-output approach and scaled small gain theorem analysis to sampled-data systems with time-varying delay. Int J Control, Automation Syst 18:1–9

    MATH  Google Scholar 

  33. Lamrabet O, Tissir EH, El Haoussi F (2019) Anti-windup compensator synthesis for sampled-data delay systems. Circuits Syst Signal Processing 38(5):2055–2071

    Article  MathSciNet  Google Scholar 

  34. Lian Z, He Y, Zhang C-K, Wu M (2020) Stability and stabilization of T-S fuzzy systems with time-varying delays via delay-product-type functional method. IEEE Trans Cybernetics 50(6):2580–2589

    Article  Google Scholar 

  35. Lin Y-C, Lo J-C (2005) Robust mixed H2/H\(_{\infty }\) filtering for discrete-time delay fuzzy systems. Int J Syst Sci 36(15):993–1006

    Article  MATH  Google Scholar 

  36. Lin C, Wang Q-G, Lee TH, Chen B (2008) H\(_{\infty }\) filter design for nonlinear systems with time-delay through T-S fuzzy model approach. IEEE Trans Fuzzy Syst 16(3):739–746

    Article  Google Scholar 

  37. Liu Y, Fang F, Park JH (2018) Decentralized dissipative filtering for delayed nonlinear interconnected systems based on T-S fuzzy model. IEEE Trans Fuzzy Syst 27(4):790–801

    Article  Google Scholar 

  38. Liu Y, Guo B-Z, Park JH, Lee S (2017) Event-based reliable dissipative filtering for T-S fuzzy systems with asynchronous constraints. IEEE Trans Fuzzy Syst 26(4):2089–2098

    Article  Google Scholar 

  39. Qiu J, Feng G, Yang J, Sun Y (2009) H\(_{\infty }\) filtering design for continuous-time nonlinear systems with interval time-varying delay via T-S fuzzy models, 7th IEEE Asian Control Conf., Hong Kong, China, pp 1006–1011

  40. Su Y, Chen B, Lin C, Zhang H (2009) A new fuzzy H\(_{\infty }\) filter design for nonlinear continuous-time dynamic systems with time-varying delays. Fuzzy Sets Syst 160(24):3539–3549

    Article  MathSciNet  MATH  Google Scholar 

  41. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst, Man, Cybernetics 15(1):116–132

    Article  MATH  Google Scholar 

  42. Wang X, Zhang X, Yang X (2019) Delay-dependent robust dissipative control for singular LPV systems with multiple input delays. Int J Control, Automation Syst 17:1–9

    Google Scholar 

  43. Wu L, Zheng WX (2009) \({\mathscr{L}}_{2}-{\mathscr{L}}_{\infty }\) fuzzy control of nonlinear fuzzy itô stochastic delay systems via dynamic output feedback. IEEE Trans. Syst., Man, Cybernetics, Part B (Cybernetics) 39(5):1308–1315

    Article  Google Scholar 

  44. Xu S, Lam J (2004) Exponential H\(_{\infty }\) filter design for uncertain Takagi-Sugeno fuzzy systems with time delay. Engineering Appl Artificial Intelligence 17(6):645–659

    Article  Google Scholar 

  45. Yang X, Mao S, Gao H, Duan Y, Zou Q (2019) Novel financial capital flow forecast framework using time series theory and deep learning : a case study analysis of Yu’e Bao transaction data. IEEE Access 7:7066–70672

    Google Scholar 

  46. Yang F, Wang Z, Hung YS (2002) Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises. IEEE Trans Automatic Control 47(7):1179–1183

    Article  MathSciNet  MATH  Google Scholar 

  47. Zhang Z, Lin C, Chen B (2016) New results on H\(_{\infty }\) filter design for nonlinear time-delay systems via fuzzy line-integral approach. Int J Fuzzy Syst 18(5):904–913

    Article  MathSciNet  Google Scholar 

  48. Zhang H, Lun S, Liu D (2007) Fuzzy H\(_{\infty }\) filter design for a class of nonlinear discrete-time systems with multiple time delays. IEEE Trans Fuzzy syst 15(3):453–469

    Article  Google Scholar 

  49. Zhang J, Xia Y, Tao R (2008) New results on H\(_{\infty }\) filtering for fuzzy time-delay systems. IEEE Trans Fuzzy Syst 17(1):128–137

    Article  Google Scholar 

  50. Zhou T, He X-Q (2015) An improved H\(_{\infty }\) filter design for nonlinear systems described by T-S fuzzy models with time-varying delay. Int J Automation Computing 12(6):671–678

    Article  Google Scholar 

  51. Zoulagh T, Boukili B, Hmamed A, El Hajjaji A (2018) Improved \({\mathscr{L}}_{2}-{\mathscr{L}}_{\infty }\) T-S fuzzy filtering for discrete stochastic systems. Int J Digital Signals Smart Syst 2(2):150–166

    Article  MATH  Google Scholar 

  52. Zoulagh T, Boukili B, Hmamed A, El Hajjaji A (2018) \({\mathscr{L}}_{2}-{\mathscr{L}}_{\infty }\) reduced-order filter design for T-S fuzzy stochastic discrete systems. Int J Syst Sci 49 (10):2061–2072

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Polydisciplinary Faculty of Safi, LPFAS Laboratory, Cadi Ayyad University, Safi, Morocco

    Said Idrissi

  2. Faculty of Sciences Dhar El Mehraz, Department of Physics, LISAC Laboratory, Sidi Mohammed Ben Abdellah University, Fez, Morocco

    Nabil El Fezazi, El Houssaine Tissir & Ismail Boumhidi

Authors
  1. Said Idrissi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nabil El Fezazi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. El Houssaine Tissir
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ismail Boumhidi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nabil El Fezazi.

Ethics declarations

Conflict of Interests

The authors declare that there is no conflict of interest.

Additional information

Publisher’s note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Idrissi, S., El Fezazi, N., Tissir, E.H. et al. H\(_{\infty }\) filter design for nonlinear systems with interval time-varying delay via T-S fuzzy models. Multimed Tools Appl 82, 25829–25846 (2023). https://doi.org/10.1007/s11042-023-14582-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-023-14582-z

Keywords

Search

Navigation