{"title":"Strict Stability of Fuzzy Differential Equations by Lyapunov Functions","authors":"Mustafa Bayram G\u00fccen, Co\u015fkun Yakar","country":null,"institution":"","volume":137,"journal":"International Journal of Computer and Information Engineering","pagesStart":315,"pagesEnd":320,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10009010","abstract":"In this study, we have investigated the strict stability
\r\nof fuzzy differential systems and we compare the classical notion of
\r\nstrict stability criteria of ordinary differential equations and the notion
\r\nof strict stability of fuzzy differential systems. In addition that, we
\r\npresent definitions of stability and strict stability of fuzzy differential
\r\nequations and also we have some theorems and comparison results.
\r\nStrict Stability is a different stability definition and this stability
\r\ntype can give us an information about the rate of decay of the
\r\nsolutions. Lyapunov’s second method is a standard technique used
\r\nin the study of the qualitative behavior of fuzzy differential systems
\r\nalong with a comparison result that allows the prediction of behavior
\r\nof a fuzzy differential system when the behavior of the null solution
\r\nof a fuzzy comparison system is known. This method is a usefull
\r\nfor investigating strict stability of fuzzy systems. First of all, we
\r\npresent definitions and necessary background material. Secondly, we
\r\ndiscuss and compare the differences between the classical notion
\r\nof stability and the recent notion of strict stability. And then, we
\r\nhave a comparison result in which the stability properties of the null
\r\nsolution of the comparison system imply the corresponding stability
\r\nproperties of the fuzzy differential system. Consequently, we give
\r\nthe strict stability results and a comparison theorem. We have used
\r\nLyapunov second method and we have proved a comparison result
\r\nwith scalar differential equations.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 137, 2018"}