On the regularization and matrix Lyapunov functions for fuzzy differential systems with uncertain parameters-Reference-Cited by-同舟云学术

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

Published:2023 Issue:10 Volume:31 Page:6089-6119
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Martynyuk Anatoliy¹,Stamov Gani²,Stamova Ivanka²,Martynyuk–Chernienko Yulya¹

Affiliation:

1. S. P. Timoshenko Institute of Mechanics, NAS of Ukraine, 3 Nesterov str., Kiev-57, Ukraine

2. Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference39 articles.

1. J. P. LaSalle, S. Lefschetz, Stability by Lyapunov's Second Method with Applications, Academic Press, New York, 1961. Available from: https://www.elsevier.com/books/stability-by-liapunovs-direct-method-with-applications-by-joseph-l-salle-and-solomon-lefschetz/la-salle/978-0-12-437056-2.

2. A. M. Lyapunov, Stability of Motion, Academic Press, New York & London, 1966. Available from: https://www.elsevier.com/books/stability-of-motion/liapunov/978-1-4832-3009-2.

3. G. Leitmann, Deterministic control of uncertain systems via a constructive use of Lyapunov stability theory, in System Modelling and Optimization, Springer, (1990), 38–55. https://doi.org/10.1007/BFb0008354

4. M. J. Lacerda, P. Seiler, Stability of uncertain systems using Lyapunov functions with non-monotonic terms, Automatica, 82 (2017), 187–193. https://doi.org/10.1016/j.automatica.2017.04.042

5. G. Stamov, I. M. Stamova, Uncertain impulsive differential systems of fractional order: almost periodic solutions, Int. J. Syst. Sci., 49 (2018), 631–638. https://doi.org/10.1080/00207721.2017.1416428