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Fuzzy Time-Delay System

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Book cover Stability and Stabilization of Linear and Fuzzy Time-Delay Systems

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 141))

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Abstract

Almost all the physical systems and processes in the real world are nonlinear [1] in nature, so over the years a considerable attention has been paid to the investigation of the dynamic behaviour of nonlinear systems. Development of nonlinear control technique has serious demerits of difficult analytical framework, computational issues and specific design for specific nonlinearity. Thus in recent times fuzzy logic control of nonlinear system [2], particularly Takagi-Sugeno (T-S) fuzzy model [3] based control has attracted attention among the researchers. It has been proved that Takagi-Sugeno (T-S) fuzzy control technique can approximate the complex nonlinear systems. T-S fuzzy modelling technique can provide a suitable representation of nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear sub-models such that it takes advantage of the advances in linear system theories. Hence the resulting stability criteria can be recast in linear matrix inequality (LMI) framework [4] which can be solved efficiently by using existing software [5].

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References

  1. H.K. Khalil, Nonlinear systems (Prentice-Hall, New Jersey, 1996), pp. 1–5

    Google Scholar 

  2. K. Tanaka, H.O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach (Wiley, New York, 2004)

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

  5. P. Gahinet, A. Nemirovski, A. Laub, M. Chilali, LMI Control Toolbox-for Use with Matlab, Natick, MA: The MATH Works (1995)

    Google Scholar 

  6. K. Gu, J. Chen, V.L. Kharitonov, Stability of Time-Delay Systems (Springer Science & Business Media, 2003)

    Google Scholar 

  7. R. Dey, S. Ghosh, G. Ray, A. Rakshit, State feedback stabilization of uncertain linear time-delay systems: a nonlinear matrix inequality approach. Numer. Linear Algebra Appl. 18(3), 351–361 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. R. Dey, S. Ghosh, G. Ray, A. Rakshit, Improved delay-dependent stabilization of time-delay systems with actuator saturation. Int. J. Robust Nonlinear Control 24(5), 902–917 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Dey, V.E. Balas, T. Lin, G. Ray, Improved delay-range-dependent stability analysis of a T-S fuzzy system with time varying delay, in 2013 IEEE 14th International Symposium on Computational Intelligence and Informatics (CINTI) (IEEE, 2013), pp. 173–178

    Google Scholar 

  10. C. Peng, D. Yue, T.-C. Yang, E.G. Tian, On delay-dependent approach for robust stability and stabilization of T-S fuzzy systems with constant delay and uncertainties. IEEE Trans. Fuzzy Syst. 17(5), 1143–1156 (2009)

    Article  Google Scholar 

  11. L. Wu, X. Su, P. Shi, Fuzzy Control Systems with Time-Delay and Stochastic Perturbation (Springer, Cham, 2015)

    Book  MATH  Google Scholar 

  12. H. Gassara, A. El Hajjaji, M. Chaabane, Robust control of T-S fuzzy systems with time-varying delay using new approach. Int. J. Robust Nonlinear Control 20(14), 1566–1578 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. L. Li, X. Liu, New results on delay-dependent robust stability criteria of uncertain fuzzy systems with state and input delays. Inf. Sci. 179(8), 1134–1148 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. F. Liu, M. Wu, Y. He, R. Yokoyama, New delay-dependent stability criteria for T-S fuzzy systems with time-varying delay. Fuzzy Sets Syst. 161(15), 2033–2042 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. S. Mobayen, An lmi-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems. Nonlinear Dyn. 79(2), 1075–1084 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  16. Y. Zhao, H. Gao, J. Lam, B. Du, Stability and stabilization of delayed T-S fuzzy systems: a delay partitioning approach. IEEE Trans. Fuzzy Syst. 17(4), 750–762 (2009)

    Article  Google Scholar 

  17. F.O. Souza, V.C. Campos, R.M. Palhares, On delay-dependent stability conditions for Takagi-Sugeno fuzzy systems. J. Franklin Inst. 351(7), 3707–3718 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. C. Peng, Y.-C. Tian, E. Tian, Improved delay-dependent robust stabilization conditions of uncertain T-S fuzzy systems with time-varying delay. Fuzzy Sets Syst. 159(20), 2713–2729 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. C. Peng, L.-Y. Wen, J.-Q. Yang, On delay-dependent robust stability criteria for uncertain T-S fuzzy systems with interval time-varying delay. Int. J. Fuzzy Syst. 13(1) (2011)

    Google Scholar 

  20. Z. Zhang, C. Lin, B. Chen, New stability and stabilization conditions for T-S fuzzy systems with time delay. Fuzzy Sets Syst. 263, 82–91 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  21. A. Seuret, F. Gouaisbaut, Wirtinger-based integral inequality: application to time-delay systems. Automatica 49(9), 2860–2866 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. P. Park, J.W. Ko, C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47(1), 235–238 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. C. Peng, Q.-L. Han, Delay-range-dependent robust stabilization for uncertain t-s fuzzy control systems with interval time-varying delays. Inf. Sci. 181(19), 4287–4299 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. E. Tian, C. Peng, Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay. Fuzzy Sets Syst. 157(4), 544–559 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  25. C.-H. Lien, K.-W. Yu, W.-D. Chen, Z.-L. Wan, Y.-J. Chung, Stability criteria for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay. IET Control Theory Appl. 1(3), 764–769 (2007)

    Article  Google Scholar 

  26. Z. Lian, Y. He, C.-K. Zhang, M. Wu, Stability analysis for T-S fuzzy systems with time-varying delay via free-matrix-based integral inequality. Int. J. Control Autom. Syst. 14(1), 21–28 (2016)

    Article  Google Scholar 

  27. E. Tian, D. Yue, Y. Zhang, Delay-dependent robust \(H_{\infty }\) control for T-S fuzzy system with interval time-varying delay. Fuzzy Sets Syst. 160(12), 1708–1719 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. X. Xia, R. Li, J. An, On delay-fractional-dependent stability criteria for Takagi-Sugeno fuzzy systems with interval delay. Math. Probl. Eng. 2014 (2014)

    Google Scholar 

  29. H.-N. Wu, H.-X. Li, New approach to delay-dependent stability analysis and stabilization for continuous-time fuzzy systems with time-varying delay. IEEE Trans. Fuzzy Syst. 15(3), 482–493 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. National Institute of Technology Silchar, Silchar, Assam, India

    Rajeeb Dey

  2. Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, India

    Goshaidas Ray

  3. “Aurel Vlaicu” University of Arad, Arad, Romania

    Valentina Emilia Balas

Authors
  1. Rajeeb Dey
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  2. Goshaidas Ray
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  3. Valentina Emilia Balas
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Correspondence to Rajeeb Dey .

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Dey, R., Ray, G., Balas, V.E. (2018). Fuzzy Time-Delay System. In: Stability and Stabilization of Linear and Fuzzy Time-Delay Systems. Intelligent Systems Reference Library, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-319-70149-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-70149-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70147-9

  • Online ISBN: 978-3-319-70149-3

  • eBook Packages: EngineeringEngineering (R0)

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