A NEW APPROACH TO STABILITY ANALYSIS OF FUZZY RELATIONAL MODEL OF DYNAMIC SYSTEMS

Document Type : Research Paper

Authors

1 Department of Electrical Engineering, Amirkabir University of Technology (AUT), P. O. Box 15914, Tehran, Iran

2 Department of Electrical Engineering, Amirk- abir University of Technology (AUT), P. O. Box 15914, Tehran, Iran

Abstract

This paper investigates the stability analysis of fuzzy relational
dynamic systems. A new approach is introduced and a set of sufficient conditions
is derived which sustains the unique globally asymptotically stable
equilibrium point in a first-order fuzzy relational dynamic system with sumproduct
fuzzy composition. This approach is also investigated for other types
of fuzzy relational composition.

Keywords


[1] J. M. Andjar and A. J. Barragn, A methodology to design stable nonlinear fuzzy control
systems, Fuzzy Sets and Systems, 154 (2005), 157-181.
[2] A. Aghili Ashtiani and M. B. Menhaj, Introducing a new pair of differentiable fuzzy norms
and its application to fuzzy relational function approximation, Proc. 10th Joint Conf. Information
Sciences, Salt Lake City, USA: World Scientific Publishing Co. ISBN: 978-981-270-
967-7, (2007), 1329-1336.
[3] A. Aghili Ashtiani and M. B. Menhaj, Numerical solution of fuzzy relational equations based
on smooth fuzzy norms, Soft Computing, 14(6) (2010), 545-557.
[4] X. Ban, X. Z. Gao, X. Huang and A. V. Vasilakos, Stability analysis of the simplest Takagi–
Sugeno fuzzy control system using circle criterion, Information Sciences, 177(20) (2007),
4387-4409.
[5] J. Chen and L. Chen, Study on stability of fuzzy closed-loop control systems, Fuzzy Sets and
Systems, 57(2) (1993), 159-168.
[6] T. Furuhashi, H. Kakami, J. Peters and W. Pedrycz, A stability analysis of fuzzy control
system using a generalized fuzzy petri net model, IEEE World Congress on Computational
Intelligence, (1998), 95-100.
[7] T. Hasegawa and T. Furuhashi, Stability analysis of fuzzy control systems simplified as a
discrete system, Int. J. Control and Cybernetics, 27(4) (1998), 565-577.
[8] K. Hirota, H. Nobuhara, K. Kawamoto and S. I. Yoshida On a lossy image compression/
reconstruction method based on fuzzy relational equation, Iranian Journal of Fuzzy Systems,
1(2) (2004), 33-42.
[9] J. B. Kiszka, M. M. Gupta and P. N. Nikiforuk, Energetic stability of fuzzy dynamic systems,
IEEE Transactions on Systems, Man and Cybernetics, 15 (1985), 783-792.
[10] A. Kandel, Y. Luo and Y. Q. Zhang, Stability analysis of fuzzy control systems, Fuzzy Sets
and Systems, 105 (1999), 33-48.
[11] C. Kolodziej and R. Priemer, Stability analysis of fuzzy systems, Journal of the Franklin
Institute, 336 (1999), 851-873.
[12] T. Leephakpreeda and C. Batur, Stability analysis of a fuzzy control system, Thammasat Int.
J. Science and Technology, 2(l) (1997), 1-5.
[13] W. Pedrycz, An identification algorithm in fuzzy relational systems, Fuzzy Sets and Systems,
13 (1984), 153-167.
[14] J. N. Ridley, I. S. Shaw and J. J. Kruger, Probabilistic fuzzy model for dynamic systems,
Electronics Letters, 24 (1988), 890-892.
[15] A. A. Suratgar and S. K. Y. Nikravesh, A new method for linguistic modeling with stability
analysis and applications, Intelligent automation and soft computing, 15(3) (2009), 329-342.
[16] A. A. Suratgar and S. K. Y. Nikravesh, Potential energy based stability analysis of fuzzy
linguistic systems, Iranian Journal of Fuzzy Systems, 2(1) (2005), 67-74.
[17] A. A. Suratgar and S. K. Y. Nikravesh, Necessary and sufficient conditions for asymptotic
stability of a class of applied nonlinear dynamical systems, Proc. 10th IEEE Int. Conf. Electronics,
Circuits and Systems, 3 (ICECS 2003), 1062-1065.
[18] A. A. Suratgar and S. K. Y. Nikravesh, A new sufficient condition for stability of fuzzy
systems, Proc. of Iranian Conf. Electrical Engineering, (2002), 441-445.
[19] E. Sanchez, Resolution of composite fuzzy relation equations, Information and Control, 30(1)
(1976), 38-48.
[20] T. ˇ Sijak, S. Teˇsnjak and O. Kuljaca, Stability analysis of fuzzy control system using describing
function method, Proc. 9th Mediterranean Conf. Control and Automation, 2001.