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Fuzzy Stability Analysis of Fuzzy Systems: A Lyapunov Approach

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Book cover Advances in Fuzzy Control

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 16))

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Abstract

The modelling phase in the analysis of the dynamic behavior of complex systems is crucial. The formalism of the model must satisfy a number of requirements. First, it must be flexible enough to capture all system properties, e.g., nonlinearities and uncertainties). Then it must allow the use of all available sources of information about the system. Finally, it must allow the analysis of the system behavior in a convenient, systematic way.

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References

  1. L. A. Zadeh: “Outline of a new approach to the analysis of complex systems and decision processes”, IEEE Trans. Syst. Man. Cybern., vol 3, pp 28–44, 1973.

    Article  MathSciNet  MATH  Google Scholar 

  2. L. A. Zadeh: “The concept of linguistic variable and its application to approximate reasoning”, Information Science, vol 8, pp 199–250, pp 301–358, vol 9, pp 43–80, 1975.

    Article  Google Scholar 

  3. E. H. Mamdani and S. Assilian: “Application of fuzzy algorithms for control of simple dynamic plant”, Proc IEE, vol 121, pp 1585–1588, 1974.

    Google Scholar 

  4. T. Takagi and M. Sugeno: “Fuzzy identification of systems and its application to modelling and control”, IEEE Trans. Syst. Man. Cybern., vol 15, pp 116–132, 1985.

    Article  MATH  Google Scholar 

  5. J. Aracil & al: “Fuzzy Control of Dynamical Systems. Stability Analysis based on Conicity Criterion”, Proc IFSA’91, Vol Engineering, Brussel, pp 5–8, 1991.

    Google Scholar 

  6. H.P. Opitz: “ Fuzzy Control and Stability criteria”, Proc EUFIT’93, Aachen, pp 130–136,1993.

    Google Scholar 

  7. L. Wang and R. Langari: “Fuzzy controller design via hypersta-bility theory”, Proc FUZZ-IEEE’94, pp 178–182, Orlando, 1994.

    Google Scholar 

  8. [ J.P Marin, A. Titli: “Robust performances of closed-loop fuzzy systems: A global Lyapunov approach”, Proc FUZZ-IEEE’96, pp 732–737, New-Orleans, 1996.

    Google Scholar 

  9. S. Boyd, L. El Gahoui, E. Feron, V. Balakrishnan: “Linear Matrix Inequalities in Systems and Control Theory”, Volume 15 of SIAM Studies in Applied Mathematics. SIAM, 1994.

    Book  Google Scholar 

  10. K. Tanaka, K. Ikeda and H.O. Wang: “Robust Stabilization of a class of Uncertain Nonlinear systems via fuzzy control: Quadratic Sta-bilizability, H Control Theory and Linear Matrix Inequalities”, IEEE Trans on Fuzzy Systems 4 (1), pp 1–13, 1996.

    Article  Google Scholar 

  11. J. Zhao, V. Wertz and R. Gorez: “Fuzzy gain scheduling based on fuzzy models”, Proc FUZZ-IEEE’96, pp 1670–1676, New-Orleans, 1996.

    Google Scholar 

  12. K. Tanaka, N. Sano: “A robust stabilization problem of fuzzy control systems and its application to backing up truck trailer”, IEEE Trans on Fuzzy Systems, pp 29–34, 1994.

    Google Scholar 

  13. K. Tanaka, M. Sugeno: “Stability analysis and design of fuzzy control system”, Fuzzy sets and systems 45, pp 135–156, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  14. J.P. Marin, A. Titli: “Necessary and Sufficient conditions for Quadratic Stability of a class of Tagaki-Sugeno Fuzzy Systems”, Proc EUFIT’95, Aachen, 1995.

    Google Scholar 

  15. W.C Kim, C.S. Ahn, W.H. Kwon: “Stability Analysis and stabilization of fuzzy state space models”, Fuzzy sets and systems, 71, pp 131–142, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  16. J.P Marin: “Conditions nécessaires et suffisantes de stabilité quadratique d’une classe de systèmes flous”, Proc LFA’95, pp 240–247, Paris, 1995.

    Google Scholar 

  17. J.P Marin: “H performance analysis of fuzzy system using quadratic storage function”, Proc AADECA’96, pp 7–11, Buenos-Aires, 1996.

    Google Scholar 

  18. J.B. Kiska, M.M. Gupta and P.N. Nikiforuk “Energistic Stability of fuzzy dynamic systems”, IEEE Trans. Syst. Man. Cybern., 5 (15), pp 783–792, 1985.

    Article  Google Scholar 

  19. E. Czogala, W. Pedrycz: “Control problems in fuzzy systems”, Fuzzy sets and systems 7, pp 257–273, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  20. C. Jianqin, C. Laijiu: “Study on stability of fuzzy closed-loop systems”, Fuzzy sets and systems 57, pp 159–168, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  21. M. De Glas: “A mathematical theory of fuzzy systems”, Fuzzy Information and Decision Process and E. Sanchez (eds.),@North-Holland Publishing Company, 1982.

    Google Scholar 

  22. M. De Glas: “Invariance and Stability of Fuzzy Systems”, Journal of Mathematical Analysis and Application, vol 99, pp 299–319, 1984.

    Article  MATH  Google Scholar 

  23. M. G. Safonov, K.J. Goh, J.H. Ly: “Control Systems synthesis via Bilinear Matrix Inequalities”, Proc ACC, pp 45–49, Baltimore, Maryland, June 1994.

    Google Scholar 

  24. M.A. Rotea, M. Corless, D. Da and I.R. Petersen: “System with structured uncertainty: Relation between Quadratic and Robust Stability”, IEEE. Trans. Aut. Cont., vol 38, n 5, pp 799–803, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  25. M. Vidyasagar: “Nonlinear Systems Analysis”, second edition, Prentice Hall, Englewood Cliffs, New Jersey 07632, 1992.

    MATH  Google Scholar 

  26. A. Van der Schaft: “L 2-gain and Passivity Techniques in Nonlinear Control”, Lecture Notes in Control and information Sciences, Vol 218, Springer, 1996.

    Book  MATH  Google Scholar 

  27. W.M. Lu, J.C. Doyle: “H Control of Nonlinear Systems: A Convex Characterization”, IEEE. Trans. Aut. Cont., vol 40, n 9, pp 1668–1675, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  28. S.G. Cao, N.W. Rees and G. Feng: “Analysis and Design of Uncertain Fuzzy Control Systems, Part II: Fuzzy Controller Design”, Proc FUZZ-IEEE’96, pp 647–653, New-Orleans, 1996.

    Google Scholar 

  29. J.P. Marin, A. Titli: “Robust Quadratic Stabilizability of Non-Homogeneous Sugeno Systems Ensuring Completeness of the Closed-loop systems”, in Proc FUZZ-IEEE’97, Barcelona, pp 185–192, 1997.

    Google Scholar 

  30. J.P. Marin, A. Titli: “ Robust Quadratic Stabilizability of fuzzy systems using fuzzy dynamic output feedback: a Matrix Inequality approach”, in Proc IFSA’97, Prague, vol 4, pp 451–456, 1997.

    Google Scholar 

  31. S.P. Wu, L. Vandenberghe ans S. Boyd: “Software for Determinant Maximization Problems, User’s Guide”, Version alpha, Stand-ford University, May 1996

    Google Scholar 

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© 1998 Springer-Verlag Berlin Heidelberg

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Marin, J.P. (1998). Fuzzy Stability Analysis of Fuzzy Systems: A Lyapunov Approach. In: Driankov, D., Palm, R. (eds) Advances in Fuzzy Control. Studies in Fuzziness and Soft Computing, vol 16. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1886-4_4

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  • DOI: https://doi.org/10.1007/978-3-7908-1886-4_4

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-11053-9

  • Online ISBN: 978-3-7908-1886-4

  • eBook Packages: Springer Book Archive

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