Open Science Research Excellence
%0 Journal Article
%A Mustafa Bayram Gücen and  Coşkun Yakar
%D 2018 
%J  International Journal of Computer, Electrical, Automation, Control and Information Engineering
%B World Academy of Science, Engineering and Technology
%I International Science Index 137, 2018
%T Strict Stability of Fuzzy Differential Equations by Lyapunov Functions
%U http://waset.org/publications/10009010
%V 137
%X In this study, we have investigated the strict stability
of fuzzy differential systems and we compare the classical notion of
strict stability criteria of ordinary differential equations and the notion
of strict stability of fuzzy differential systems. In addition that, we
present definitions of stability and strict stability of fuzzy differential
equations and also we have some theorems and comparison results.
Strict Stability is a different stability definition and this stability
type can give us an information about the rate of decay of the
solutions. Lyapunov’s second method is a standard technique used
in the study of the qualitative behavior of fuzzy differential systems
along with a comparison result that allows the prediction of behavior
of a fuzzy differential system when the behavior of the null solution
of a fuzzy comparison system is known. This method is a usefull
for investigating strict stability of fuzzy systems. First of all, we
present definitions and necessary background material. Secondly, we
discuss and compare the differences between the classical notion
of stability and the recent notion of strict stability. And then, we
have a comparison result in which the stability properties of the null
solution of the comparison system imply the corresponding stability
properties of the fuzzy differential system. Consequently, we give
the strict stability results and a comparison theorem. We have used
Lyapunov second method and we have proved a comparison result
with scalar differential equations.
%P 315 - 319