Stability analysis of impulsive fuzzy differential equations with finite delayed state

Subject Areas : Statistics

D. Naseh ^{1 *} , N. Pariz ² , A. Vahidian Kamyad ³

1 - PhD, Department of Electrical Engineering (Control), Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
2 - Professor, Department of Electrical Engineering (Control), Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
3 - Professor, Department of Applied Mathematics, Faculty of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

Received: 2017-12-20 Accepted : 2018-09-01 Published : 2018-10-23

Keywords: دستگاه معادلات دیفرانسیل فازی, قضیه مقایسه, توابع شبه لیاپانوف برداری, غیرنزولی شبه یکنوای فوقانی, پایداری کاربردی,

Abstract :

In this paper we introduce some stability criteria for impulsive fuzzy system of differential equations with finite delay in states. Firstly, a new comparison principle for fuzzy differential system compared to crisp ordinary differential equation, based on a notion of upper quasi-monotone nondecreasing, in N dimentional state space is presented. Furthermore, in order to analyze the stability of fuzzy dynamical systems, vector Lyapunov like functions are defined. Then, by using these vector Lyapunov-like functions together with the new comparison theorem which is presented before, we will get results for some concepts of stability (eventual stability, asymptotic stability, strong stability, uniform stability and their combinations) for impulsive fuzzy delayed system of differential equations. Moreover, some theorems for practical stability in terms of two measures are introduced and are proved. Finally, an illustrating example for stability checking of a system of differential equations with fuzziness and time delay in states is given.

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