Invariance Principle, S-procedure and the Asymptotic Behavior of T-S Fuzzy Systems
DOI:
https://doi.org/10.5540/03.2025.011.01.0415Palabras clave:
T-S Fuzzy Systems, Extended LaSalle Principle, Linear Matrix InequalityResumen
In this paper, the asymptotic behavior of nonlinear dynamical systems is studied by means of a T-S fuzzy system, which exactly represents the nonlinear system in question, and the extended Invariance Principle. We use the S-Procedure to obtain less conservative conditions than those presented in [2] to estimate the attracting invariant set in terms of Linear Matrix Inequalities.
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L. F. Alberto. “O Princípio de Invariância de LaSalle estendido aplicado ao estudo de coerência de geradores e à análise de estabilidade transitória multi-’swing’.” PhD thesis. São Carlos: Universidade de São Paulo, 2000.
R. Araujo, L. F. C. Alberto, and M. C. Valentino. “Invariance Principle and the Asymptotic Behavior of T-S Fuzzy Systems”. In: Proceeding Series of the Brazilian Society of Computational and Applied Mathematics. 2023, pp. 010063-1–7. doi:10.5540/03.2023.010.01.0063.
I. Pólik and T. Terlaky. “A Survey of the S-Lemma”. In: SIAM Review 49.3 (2007), pp. 371–418. doi:10.1137/S003614450444614X.
K. Tanaka and H. O. Wang. Fuzzy Control Systems Design and Analysis. 2001. isbn:0-471-32324-1.
T. Taniguchi, K. Tanaka, H. Ohtake, and H. O. H. Wang. “Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems”. In: IEEE Transactions on Fuzzy Systems 9.4 (2001), pp. 525–538. doi:10.1109/91.940966.
M. C. Valentino, F. A. Faria, V. A. Oliveira, and L. F. Alberto. “Ultimate boundedness sufficient conditions for nonlinear systems using TS fuzzy modelling”. en. In: Fuzzy Sets and Systems 361 (Apr. 2019), pp. 88–100. issn:01650114. doi:10.1016/j.fss.2018.03.010.
M. Yang, S. Wang, and Y. Xia. “Non-quadratic extension of homogeneous S-lemma and its applications in optimization”. In: Journal of Industrial and Management Optimization 19.9 (2023), pp. 6826–6834. doi:10.3934/jimo.2022241.
