Skip to main content
SpringerLink
Log in

A switching control approach for stability analysis of constrained T–S fuzzy systems

  • Research
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, the stabilization problem of Takagi–Sugeno (T–S) fuzzy system with input constraints is investigated via a membership function-dependent Lyapunov function (MFDLF). First of all, a membership function-dependent sector condition is adopted to address the input saturation. Then, the average dwell-time (ADT) switching technique is applied to handle the time derivatives of the membership functions, which significantly reduces the conservativeness of the results. Next, on the basis of Lyapunov stability tool, the necessary conditions for the exponential stability are proposed under a non-PDC fuzzy control scheme. Furthermore, the polynomial membership function-dependent matrices are introduced, which achieves the extension of the linear switching to quadratic switching, and further relaxes the conditions. Finally, numerical simulation examples are given for verification.

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
Fig. 4

Similar content being viewed by others

Data availability

No datasets were generated or analysed during the current study.

References

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

    Article  Google Scholar 

  2. Wang, L.X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Prentice-Hall Inc (1994)

    Google Scholar 

  3. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM (1994)

    Book  Google Scholar 

  4. Hu, T., Lin, Z., Chen, B.M.: An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica 38(2), 351–359 (2002)

    Article  Google Scholar 

  5. Lee, S.M., Kwon, O.M., Park, J.H.: Regional asymptotic stability analysis for discrete-time delayed systems with saturation nonlinearity. Nonlinear Dyn. 67(1), 885–892 (2012)

    Article  MathSciNet  Google Scholar 

  6. Nguyen, A.-T., Dambrine, M., Lauber, J.: Lyapunov-based robust control design for a class of switching non-linear systems subject to input saturation: application to engine control. IET Control Theory Appl. 8(17), 1789–1802 (2014)

    Article  MathSciNet  Google Scholar 

  7. Tarbouriech, S., Garcia, G., da Silva Jr, J.M.G., Queinnec, I.: Stability and Stabilization of Linear Systems with Saturating Actuators. Springer (2011)

    Book  Google Scholar 

  8. Cao, Y.-Y., Lin, Z.: Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation. IEEE Trans. Fuzzy Syst. 11(1), 57–67 (2003)

    Article  Google Scholar 

  9. Da Silva, J.G., Tarbouriech, S., Reginatto, R.: Analysis of regions of stability for linear systems with saturating inputs through an anti-windup scheme. In: Proceedings of the International Conference on Control Applications, 2, 1106–1111 IEEE (2002)

  10. Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality approach. Wiley (2004)

    Google Scholar 

  11. Da Silva, J.G., Tarbouriech, S.: Antiwindup design with guaranteed regions of stability: an LMI-based approach. IEEE Trans. Autom. Control 50(1), 106–111 (2005)

    Article  MathSciNet  Google Scholar 

  12. Montagner, V.F., Oliveira, R.C.L.F., Peres, P.L.D.: Convergent LMI relaxations for quadratic stabilizability and \({{\mathscr {H}}}_{\infty }\) control of Takagi–Sugeno fuzzy systems. IEEE Trans. Fuzzy Syst. 17(4), 863–873 (2009)

    Article  Google Scholar 

  13. Vafamand, N., Asemani, M.H., Khayatiyan, A.: A robust \({{\cal{L} }}_{1}\) controller design for continuous-time TS systems with persistent bounded disturbance and actuator saturation. Eng. Appl. Artif. Intell. 56, 212–221 (2016)

    Article  Google Scholar 

  14. Hussain, M., Rehan, M., Ahn, C.K., Zheng, Z.: Static anti-windup compensator design for nonlinear time-delay systems subjected to input saturation. Nonlinear Dyn. 95(3), 1879–1901 (2019)

    Article  Google Scholar 

  15. Guerra, T.M., Vermeiren, L.: LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi–Sugeno’s form. Automatica 40(5), 823–829 (2004)

    Article  MathSciNet  Google Scholar 

  16. Zeng, Y., Lam, H.-K., Xiao, B., Wu, L.: Tracking control for nonlinear systems with actuator saturation via interval type-2 T-S fuzzy framework. IEEE Trans. Cybern. 53(11), 7085–7094 (2023)

    Article  Google Scholar 

  17. Mozelli, L.A., Palhares, R.M., Avellar, G.S.: A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems. Inf. Sci. 179(8), 1149–1162 (2009)

    Article  MathSciNet  Google Scholar 

  18. Kim, S.H.: Toward less conservative stability and stabilization conditions for T-S fuzzy systems. Nonlinear Dyn. 75(4), 621–632 (2014)

    Article  MathSciNet  Google Scholar 

  19. Kennouche, A., Saifia, D., Chadli, M., Labiod, S.: Adaptive fuzzy observer based non-quadratic control for nonlinear system subject to actuator faults and saturation. J. Franklin Inst. 360(8), 5411–5441 (2023)

    Article  MathSciNet  Google Scholar 

  20. Nguyen, A.-T., Márquez, R., Dequidt, A.: An augmented system approach for LMI-based control design of constrained Takagi–Sugeno fuzzy systems. Eng. Appl. Artif. Intell. 61, 96–102 (2017)

    Article  Google Scholar 

  21. Kim, S.H.: Local nonquadratic stabilization of T-S fuzzy systems via improved slack-variable-free relaxation technique under a limited operating region. Nonlinear Dyn. 111(13), 12233–12251 (2023)

    Article  Google Scholar 

  22. Nguyen, A.-T., Laurain, T., Palhares, R., Lauber, J., Sentouh, C., Popieul, J.-C.: LMI-based control synthesis of constrained Takagi–Sugeno fuzzy systems subject to \({{\cal{L}}}_{2}\) or \({{\cal{L} }}_{\infty }\) disturbances. Neurocomputing 207, 793–804 (2016)

  23. Zou, T., Li, S.: Stabilization via extended nonquadratic boundedness for constrained nonlinear systems in Takagi–Sugeno’s form. J. Franklin Inst. 348(10), 2849–2862 (2011))

  24. Tiko, S., Mesquine, F.: Constrained control for a class of TS fuzzy systems. IEEE Trans. Fuzzy Syst. 31(1), 348–353 (2022))

  25. Pan, J.-T., Guerra, T.M., Fei, S.-M., Jaadari, A.: Nonquadratic stabilization of continuous T-S fuzzy models: LMI solution for a local approach. IEEE Trans. Fuzzy Syst. 20(3), 594–602 (2012)

    Article  Google Scholar 

  26. Wang, L., Lam, H.K.: H\(\infty \) control for continuous-time Takagi-Sugeno fuzzy model by applying generalized Lyapunov function and introducing outer variables. Automatica 125, 109409 (2021)

    Article  MathSciNet  Google Scholar 

  27. Wang, L., Liu, J., Lam, H.-K.: New results of observer design for continuous-time fuzzy systems: a switching technique. IEEE Trans. Syst. Man Cybern. Syst. 52(9), 5702–5706 (2021)

    Article  Google Scholar 

  28. Lopes, A.N., Leite, V.J., Silva, L.F., Guelton, K.: Anti-windup TS fuzzy PI-like control for discrete-time nonlinear systems with saturated actuators. Int. J. Fuzzy Syst. 22(1), 46–61 (2020)

    Article  Google Scholar 

  29. Zare, I., Asemani, M.H., Setoodeh, P.: Active adaptive observer-based fault-tolerant control strategy for a class of T-S fuzzy systems with unmeasurable premise variables. IEEE Trans. Fuzzy Syst. 31(10), 3543–3554 (2023)

    Article  Google Scholar 

  30. Silva, L.F., Leite, V.J., Castelan, E.B., Klug, M., Guelton, K.: Local stabilization of nonlinear discrete-time systems with time-varying delay in the states and saturating actuators. Inf. Sci. 518, 272–285 (2020)

    Article  MathSciNet  Google Scholar 

  31. Liberzon, D.: Switching in Systems and Control, vol. 190. Springer (2003)

    Book  Google Scholar 

  32. Mozelli, L.A., Palhares, R.M., Souza, F., Mendes, E.M.: Reducing conservativeness in recent stability conditions of TS fuzzy systems. Automatica 45(6), 1580–1583 (2009)

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 62173123, in part by the Natural Science Foundation of Hebei Province under Grant F2021202045, and in part by the Natural Science Foundation of Tianjin under Grant 23JCYBJC00930.

Author information

Authors and Affiliations

  1. School of Artificial Intelligence, Hebei University of Technology, Tianjin, 300401, China

    Weihua Wang & Likui Wang

  2. Institute of Advanced Technology Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Xiangpeng Xie

  3. Department of Engineering, King’s College London, Strand, London, WC2R 2LS, UK

    Hak-Keung Lam

Authors
  1. Weihua Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Likui Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiangpeng Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hak-Keung Lam
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. The main idea and method were proposed by [Likui Wang]. The first draft of the manuscript was written by [Weihua Wang]. [Xiangpeng Xie] and [Hak-Keung Lam] commented on previous versions of the manuscript. All authors read and approved the final manuscript

Corresponding author

Correspondence to Likui Wang.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

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

Wang, W., Wang, L., Xie, X. et al. A switching control approach for stability analysis of constrained T–S fuzzy systems. Nonlinear Dyn 112, 8249–8259 (2024). https://doi.org/10.1007/s11071-024-09507-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-024-09507-w

Keywords

Search

Navigation