On the regularization and matrix Lyapunov functions for fuzzy differential systems with uncertain parameters

Autor:	Anatoliy Martynyuk, Gani Stamov, Ivanka Stamova, Yulya Martynyuk–Chernienko
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	fuzzy systems regularization scheme boundedness stability matrix lyapunov functions Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 31, Iss 10, Pp 6089-6119 (2023)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2023310?viewType=HTML
Popis:	In this paper, for a regularized fuzzy system, a generalization of the direct Lyapunov method is adapted on the base of matrix-valued Lyapunov-like functions. First, the new concept of a regularization scheme for fuzzy systems is discussed and the matrix-valued Lyapunov function technique is introduced. Then, sufficient conditions are established for the boundedness and stability of the equilibrium set of solutions of the regularized fuzzy system of differential equations. Scalar and vector Lyapunov-type functions are used based on an auxiliary matrix-valued function. Finally, a discussion is offered for the future directions of the proposed approach. Since the strategies for the analysis of the stability of fuzzy models are very important in numerous aspects, we expect that our results will inspire researchers to develop the introduced concept.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/1abe6b107861482fbd1527a74fd6cd69 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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