Abstract
The robust stability margin of fuzzy-coefficient polynomials is determined. Since the membership level of a fuzzy number is expressed by a functional interval, the method applied to analyze the robust stability of interval polynomials can be applied to solve this problem. A new method for computing the robust stability margin of fuzzy polynomials with a convenient graphic interpretation is developed on the basis of the Tsypkin-Polyak robust stability criterion and D-decomposition of interval polynomials. It can also be used to find the degree to which the membership level of every coefficient can be varied without violating the stability of a system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Tsypkin, Ya.Z., Osnovy teorii avtomaticheskikh sistem (Principles of Automatic Control Systems), Moscow: Nauka, 1977.
Pervozvanskii, A.A., Kurs teorii avtomaticheskogo upravleniya (A Course in Automatic Control Theory), Moscow: Nauka, 1986.
Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
Tsypkin, Ya.Z. and Polyak, B.T., Frequency Domain Criteria for l p-Robust Stability of Continuous Linear Systems, IEEE Trans. Automat. Control, 1991, vol. 36, pp. 1464–1469.
Zadeh, L.A., A New Approach to Analysis of Complex Systems and Decision Making Processes, in Matematika segodnya (Matematics Today), Moscow: Znanie, 1974.
Zadeh, L., The Concept of a Linguistic Variable and Its Application to Approximate Reasoning, New York: Elsevier, 1973. Translated under the title Ponyatie lingvisticheskoi peremennoi i ego primenenie dlya prinyatiya priblizhennykh reshenii, Moscow: Mir, 1976.
Averkin, A.N., Batyrshin, I.Z., Blishun, A.F., et al., Nechetkie mnozhestva v modelyakh upravleniya i iskusstvennogo intellekta (Fuzzy Sets in Control and Artificial Intelligence Models), Moscow: Nauka, 1986.
Asai, K., et al., Applied Fuzzy Systems, Boston: AP Professional, 1994. Translated under the title Prikladnye nechetkie sistemy, Moscow: Mir, 1993.
The Handbook of Fuzzy Sets, Dubois, D. and Prade, H., Eds., Dordrecht: Kluwer, 2000.
A Special Issue “Interfaces between Fuzzy Set Theory and Interval Analysis,” Fuzzy Sets Syst., 2003, vol. 135.
Bondia, J. and Pico, J., Analysis of Linear Systems with Fuzzy Parametric Uncertainty, Fuzzy Sets Syst., 2003, vol. 135, pp. 81–121.
Argoun, M.B., Frequency Domain Conditions for the Stability of Perturbed Polynomials, IEEE Trans. Automat. Control, 1987, AC-32, vol. 10, pp. 913–916.
Petrov, N.P. and Polyak, B.T., Robust D-Decomposition, Avtom. Telemekh., 1991, no. 11, pp. 41–53.
Author information
Authors and Affiliations
Additional information
Translated from Avtomatika i Telemekhanika, No. 4, 2005, pp. 98–109.
Original Russian Text Copyright © 2005 by Le Hung Lan.
This paper was recommended for publication by B.T. Polyak, a member of the Editorial Board
Rights and permissions
About this article
Cite this article
Lan, L.H. Robust stability of fuzzy-parameter systems. Autom Remote Control 66, 596–605 (2005). https://doi.org/10.1007/s10513-005-0103-4
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10513-005-0103-4