We propose a general principle of comparison for stability-preserving mappings and establish sufficient conditions of stability for the Takagi – Sugeno continuous fuzzy systems.
References
T. Takagi and M. Sugeno, “Fuzzy identification of systems and its application to modeling and control,” IEEE Trans. Syst., Man, Cybern., 15, 116–132 (1985).
X. J. Zeng and M. G. Singh, “Approximation theory of fuzzy systems — MIMO case,” IEEE Trans. Fuzzy Syst., 3, No. 2, 219–235 (1995).
M. Benrejeb, M. Gasmi, and P. Borne, “New stability conditions for TS fuzzy continuous nonlinear models,” Nonlin. Dynam. Syst. Theory, 5, No. 4, 369–379 (2005).
J.-Y. Dieulot, “Design of stable controllers for Takagi–Sugeno systems with concentric characteristic regions,” Nonlin. Dynam. Syst. Theory, 3, No. 1, 65–74 (2003).
Hui Ye, A. N. Michel, and Ling Hou, “Stability theory for hybrid dynamical systems,” IEEE Trans. Autom. Contr., 43, No. 4, 461–474 (1998).
Z. Li and C. B. Soh, “Lyapunov stability of discontinuous dynamic systems,” IMA J. Math. Contr. Inform., 16, 261–274 (1999).
A. N. Michel, K. Wang, and B. Hu, Qualitative Theory of Dynamical Systems, Dekker, New York (2001).
A. A. Martynyuk, “On the stability of motion of discontinuous dynamical systems,” Dokl. Akad. Nauk Ross., 397, No. 3, 308–312 (2004).
Guisheng Zhai, Bo Hu, Sun Ye, and A. N. Michel, “Analysis of time-controlled switched systems by stability,” Nonlin. Dynam. Syst. Theory, 2, No. 2, 203–213 (2002).
R. Horn and C. Johnson, Matrix Analysis, Cambridge Univ. Press, Cambridge (1985).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 5, pp. 641–649, May, 2009.
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Denisenko, V.S., Martynyuk, A.A. & Slyn’ko, V.I. On the mappings preserving the Lyapunov stability of Takagi–Sugeno fuzzy systems. Ukr Math J 61, 764–774 (2009). https://doi.org/10.1007/s11253-009-0243-8
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DOI: https://doi.org/10.1007/s11253-009-0243-8