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JACIII Vol.30 No.3 pp. 931-939
(2026)
doi: 10.20965/jaciii.2026.p0931

Research Paper:

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Unknown Input Observer Designs for Polynomial Fuzzy Systems with Uncertainties

Xiang Wang ORCID Icon, Lizhen Li† ORCID Icon, and Yutang Wu

College of Mathematics and Physics, Shanghai University of Electric Power
No.1851 Hucheng Ring Road, Pudong New Area, Shanghai 201306, China

†Corresponding author

Received:
March 23, 2025
Accepted:
February 12, 2026
Published:
May 20, 2026
Creative Commons License
Keywords:
unmeasurable state variables, unknown input observer, uncertain nonlinear systems, slack matrices
Abstract

This study developed a novel design framework for unknown input observers in uncertain polynomial fuzzy systems using the sum-of-squares algorithm. First, both the system and the input matrices depended on unmeasurable state variables that required estimation. Secondly, the observer structure in this study differed from existing formulations. The proposed observer eliminated uncertainty effects without requiring explicit bounds or auxiliary controllers. The incorporation of slack matrices facilitated the resolution of non-convex terms in the stability conditions, thereby reducing design conservatism. Finally, a simulation study was conducted, and the results confirmed the validity and theoretical value of the developed strategy.

Errors converge globally

Errors converge globally

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Cite this article as:
X. Wang, L. Li, and Y. Wu, “Unknown Input Observer Designs for Polynomial Fuzzy Systems with Uncertainties,” J. Adv. Comput. Intell. Intell. Inform., Vol.30 No.3, pp. 931-939, 2026.
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References
  1. [1] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. on Syst. Man Cybern., Vol.15, No.1, pp. 116-132, 1985. https://doi.org/10.1109/TSMC.1985.6313399
  2. [2] M. Sugeno and G. T. Kang, “Structure identification of fuzzy model,” Fuzzy Sets Syst., Vol.28, No.1, pp. 15-33, 1988. https://doi.org/10.1016/0165-0114(88)90113-3
  3. [3] M. Xu, J. Gu, and Z. Xu, “Observer-based switching control for T–S fuzzy systems with mixed time delays,” Int. J. of Fuzzy Systems, Vol.25, No.4, pp. 1480-1494, 2023. https://doi.org/10.1007/s40815-022-01447-0
  4. [4] B. J. Rhee and S. Won, “A new fuzzy Lyapunov function approach for a Takagi–Sugeno fuzzy control system design,” Fuzzy Sets Syst., Vol.157, No.9, pp. 1211-1228, 2006. https://doi.org/10.1016/j.fss.2005.12.020
  5. [5] K. Tanaka, H. Yoshida, and H. Ohtake, “A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems,” IEEE Trans. on Fuzzy Syst., Vol.17, No.4, pp. 911-922, 2009. https://doi.org/10.1109/TFUZZ.2008.924341
  6. [6] K. Tanaka, H. Ohtake, and H. O. Wang, “Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach,” IEEE Trans. on Syst. Man Cybern., Vol.39, No.2, pp. 561-567, 2009. https://doi.org/10.1109/TSMCB.2008.2006639
  7. [7] H. K. Lam, M. Narimani, and H. Li, “Stability analysis of polynomial-fuzzy-model-based control systems using switching polynomial Lyapunov function,” IEEE Trans. on Fuzzy Syst., Vol.21, No.5, pp. 800-813, 2013. https://doi.org/10.1109/TFUZZ.2012.2230005
  8. [8] K. Y. Ye, J. Li, and Y. G. Niu. “Disturbance-observer-based sliding mode control for polynomial fuzzy systems,” Int. J. of Systems Science, pp. 1-5, 2025. https://doi.org/10.1080/00207721.2025.2491780
  9. [9] B. Pang and Q. Zhang, “Interval observers design for polynomial fuzzy singular systems by utilizing sum-of-squares program,” IEEE Trans. Systs., Man, Cybern., Syst., Vol.50, No.6, pp. 1999-2006, 2020. https://doi.org/10.1109/TSMC.2018.2790975
  10. [10] D. Pylorof, E. Bakolas, and K. S. Chan, “Design of robust Lyapunov-based observers for nonlinear systems with sum-of-squares programming,” IEEE Control Syst. Letters, Vol.4, No.2, pp. 283-288, 2019. https://doi.org/10.1109/LCSYS.2019.2925511
  11. [11] H. Han, Y. Sueyama, and C. Chen, “A design of observers of control state and uncertainty via transformation of T-S fuzzy models,” J. Adv. Comput. Intell. Intell. Inform., Vol.22, No.2, pp. 194-202, 2018. https://doi.org/10.20965/jaciii.2018.p0194
  12. [12] F. Sabbaghian and M. Farrokhi, “Polynomial fuzzy observer-based integrated fault estimation and fault tolerant control with uncertainty and disturbance,” IEEE Trans. Fuzzy Syst., Vol.30, No.3, pp. 741-754, 2020. https://doi.org/10.1109/TFUZZ.2020.3048505
  13. [13] X. Wang, L. Li, and Y. Wu, “Static output feedback controller design for switching polynomial fuzzy time-varying delay system,” J. Adv. Comput. Intell. Intell. Inform., Vol.28, No.6, pp. 1335-1343, 2024. https://doi.org/10.20965/jaciii.2024.p1335
  14. [14] V. P. Vu and W. J. Wang, “State and disturbance observer-based controller synthesis for polynomial system,” 2017 Int. Conf. on System Science and Engineering (ICSSE), pp. 66-70, 2017. https://doi.org/10.1109/ICSSE.2017.8030839
  15. [15] V. P. Vu, W. J. Wang, H. C. Chen, and J. M. Zurada, “Unknown input-based observer synthesis for a polynomial T-S fuzzy model system with uncertainties,” IEEE Trans. Fuzzy Syst., Vol.26, No.3, pp. 1447-1458, 2018. https://doi.org/10.1109/TFUZZ.2017.2724507
  16. [16] T. Seo, H. Ohtake, K. Tanaka, Y. J. Chen, and H. O. Wang, “A polynomial observer design for a wider class of polynomial fuzzy systems,” 2011 IEEE Int. Conf. on Fuzzy Systems, pp. 1305-1311, 2011. https://doi.org/10.1109/FUZZY.2011.6007342
  17. [17] K. Tanaka, H. Ohtake, and T. Seo, “Polynomial fuzzy observer designs: A sum-of-squares approach,” IEEE Trans. Syst. Man Cybern. Part B, Vol.42, No.5, pp. 1330-1342, 2012. https://doi.org/10.1109/TSMCB.2012.2190277
  18. [18] N. Azman, S. Saat, and S. K. Nguang, “Nonlinear observer design with integrator for a class of polynomial discrete-time systems,” 2015 Int. Conf. on Computer, Communications, and Control Technology, pp. 422-426, 2015. https://doi.org/ 10.1109/I4CT.2015.7219611
  19. [19] Y. Wang, H. Zhang, and J. Zhang, “An SOS-based observer design for discrete-time polynomial fuzzy systems,” Int. J. of Fuzzy Syst., Vol.17, No.1, pp. 94-104, 2015. https://doi.org/10.1007/s40815-015-0003-x
  20. [20] J. Zhao and H. Han, “A control approach based on observers of state and uncertainty for a class of Takagi–Sugeno fuzzy models,” J. Adv. Comput. Intell. Intell. Inform., Vol.25, No.3, pp. 317-325, 2021. https://doi.org/10.20965/jaciii.2021.p0317
  21. [21] W. J. Wang, V. P. Vu, and W. Chang, “A synthesis of observer-based controller for stabilizing uncertain T-S fuzzy systems,” J. of Intell. Fuzzy Syst., Vol.30, No.6, pp. 3451-3463. https://doi.org/10.1049/iet-cta.2017.0489
  22. [22] A. Golabi, M. Beheshti, and M. Asemani, “ H_infty H∞ robust fuzzy dynamic observer-based controller for uncertain Takagi–Sugeno fuzzy systems,” IET Control Theory and Applications, Vol.6, No.10, pp. 1434-1444, 2011 https://doi.org/10.1049/iet-cta.2011.0435
  23. [23] T. Dang, W. J. Wang, and C. H. Huang, “Observer synthesis for the T-S fuzzy system with uncertainty and output disturbance,” J. of Intell. Fuzzy Syst., Vol.22, No.4, pp. 173-183, 2011. https://doi.org/10.3233/IFS-2011-0474
  24. [24] V. P. Vu and W. J. Wang, “Observer synthesis for uncertain Takagi–Sugeno fuzzy systems with multiple output matrices,” IET Control Theory and Applications, Vol.10, No.2, pp. 151-161, 2016. https://doi.org/10.1049/iet-cta.2015.0228
  25. [25] J. S. Yeh, W. Chang, and W. J. Wang, “Unknown input based observer synthesis for uncertain Takagi–Sugeno fuzzy systems,” IET Control Theory and Applications, Vol.9, No.5, pp. 729-735, 2015. https://doi.org/10.1049/iet-cta.2014.0705
  26. [26] V. P. Vu and W. J. Wang, “Observer design for a discrete-time T-S fuzzy system with uncertainties,” 2015 IEEE Int. Conf. on Automation Science and Engineering, pp. 1262-1267, 2015. https://doi.org/10.1109/CoASE.2015.7294272
  27. [27] H. S. Kim, J. B. Park, and Y. H. Joo, “Robust stabilization condition for a polynomial fuzzy system with parametric uncertainties,” 2012 12th Int. Conf. on Control, Automation and Systems, pp. 107-111, 2012.
  28. [28] K. Tanaka, M. Tanaka, Y. J. Chen, and H. O. Wang, “A new sum-of-squares design framework for robust control of polynomial fuzzy systems with uncertainties,” IEEE Trans. Fuzzy Systs., Vol.24, No.1, pp. 94-110, 2016. https://doi.org/10.1109/TFUZZ.2015.2426719
  29. [29] A. Chibani, M. Chadli, M. M. Belhaouane, and N. B. Braiek, “Polynomial observer design for unknown inputs polynomial fuzzy systems: A sum of squares approach,” IEEE Conf. on Decision and Control, pp. 6788-6793, 2015. https://doi.org/10.1109/CDC.2014.7040455
  30. [30] A. Chibani, M. Chadli, and N. B. Braiek, “A sum of squares approach for polynomial fuzzy observer design for polynomial fuzzy systems with unknown inputs,” Int. J. of Control Auto. and Syst., Vol.14, No.1, pp. 323-330, 2016. https://doi.org/10.1007/s12555-014-0406-8

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Last updated on May. 20, 2026