Parametric Uncertainty of Linear Discrete-Time Systems Described by Fuzzy Numbers

1. Bondia, J., Picó, J.: Analysis of Systems with Variable Parametric Uncertainty Using Fuzzy Functions. In: Proc. of European Control Conference, ECC 1999 (1999)

   Google Scholar 

2. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, Inc., London (1980)

   MATH  Google Scholar 

3. Nguyen, H.T., Kreinovich, V.: How stable is a fuzzy linear system. In: Proc. 3rd IEEE Conf. on Fuzzy Systems, pp. 1023–1027 (1994)

   Google Scholar 

4. Bondia, J., Picó, J.: Analysis of linear systems with fuzzy parametric uncertainty. Fuzzy Sets and Systems 135, 81–121 (2003)

   Article  MathSciNet  MATH  Google Scholar 

5. Argoun, M.B.: Frequency domain conditions for the stability of perturbed polynomials. IEEE Trans. Automat. Control 10, 913–916 (1987)

   Article  MATH  Google Scholar 

6. Lan, L.: Robust stability of fuzzy-parameter systems. Automation and Remote Control 66, 596–605 (2005)

   Article  MathSciNet  MATH  Google Scholar 

7. Hušek, P.: Generalized Tsypkin-Polyak locus. In: Proc. of 2nd IFAC Symposium on System, Structure and Control, SSSC 2004, pp. 78–83 (2004)

   Google Scholar 

8. Tsypkin, Y.Z., Polyak, B.T.: Frequency domain criterion for robust stability of polytope of polynomials. In: Mansour, M., Balemi, S., Truol, W. (eds.) Control of Uncertain Dynamic Systems, pp. 113–124. Birkhauser, Basel (1992)

   Google Scholar 

9. Mansour, M.: On robust stability of linear systems. Systems & Control Letters 22, 137–143 (1994)

   Article  MathSciNet  MATH  Google Scholar 

10. Cieslik, J.: On possibilities of the extension of Kharitonov’s stability test for interval polynomials to discrete-time case. IEEE Transactions on Automatic Control 32, 237–238 (1987)

    Article  MathSciNet  Google Scholar 

11. Mansour, M., Kraus, F.J., Anderson, B.D.O.: Strong Kharitonov theorem for discrete systems. In: Milanese, M., Temp, R., Vicino, A. (eds.) Robustness in Identification and Control, vol. 22, pp. 113–124. Plenum Press, New York (1989)

    Google Scholar 

12. Kraus, F.J., Anderson, B.D.O., Mansour, M.: Robust Schur polynomial stability and Kharitonov theorem. International Journal of Control 47, 1213–1225 (1988)

    Article  MathSciNet  MATH  Google Scholar 

13. Greiner, R.: Necessary conditions for Schur-stability of interval polynomials. IEEE Transactions on Automatic Control 49, 740–744 (2004)

    Article  MathSciNet  Google Scholar 

14. Bhattacharyya, S.P., Chapellat, H., Keel, L.: Robust Control: The Parametric Approach. Prentice-Hall, Inc., Upper Saddle River (1995)

    MATH  Google Scholar 

15. Jury, E.: A modified stability table for linear discrete systems. Proc. IEEE 53, 184–185 (1965)

    Article  Google Scholar 

16. Ogata, K.: Discrete-time control systems (2nd ed.), 2nd edn. Prentice-Hall, Inc., Upper Saddle River (1995)

    Google Scholar 

17. Shiomi, K., Otsuka, N., Inaba, H., Ishii, R.: The property of bilinear transformation matrix and Schur stability for a linear combination of polynomials. Journal of Franklin Institute 336, 533–541 (1999)

    Article  MathSciNet  MATH  Google Scholar 

18. Jalili-Kharaajoo, M., Araabi, B.N.: The Schur stability via the Hurwitz stability analysis using a biquadratic transformation. Automatica 41, 173–176 (2005)

    Article  MathSciNet  MATH  Google Scholar 

19. Kiselev, O., Lan, L., Polyak, B.: Frequency responses under parametric uncertainties. Automation and Remote Control 58, 645–661 (1997)

    MathSciNet  MATH  Google Scholar 

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