Stability analysis of impulsive fuzzy differential equations with finite delayed state

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Naseh D.; PARIZ N.; VAHIDIAN KAMYAD A.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2018 | Volume:4 | Issue:15 Page(s): 105-119

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Title

Stability analysis of impulsive fuzzy differential equations with finite delayed state

Author(s)

Naseh D. | PARIZ N. | VAHIDIAN KAMYAD A. | Issue Writer Certificate

Keywords

System of fuzzy differential equationsQ1

Comparison theoremQ1

Vector Lyapunov-like functionQ1

Upper quasi-monotone nondecreasingQ1

Practical stabilityQ1

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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APA: Copy

Naseh, D., PARIZ, N., & VAHIDIAN KAMYAD, A.. (2018). Stability analysis of impulsive fuzzy differential equations with finite delayed state. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 4(15 ), 105-119. SID. https://sid.ir/paper/257290/en

Vancouver: Copy

Naseh D., PARIZ N., VAHIDIAN KAMYAD A.. Stability analysis of impulsive fuzzy differential equations with finite delayed state. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2018;4(15 ):105-119. Available from: https://sid.ir/paper/257290/en

IEEE: Copy

D. Naseh, N. PARIZ, and A. VAHIDIAN KAMYAD, “Stability analysis of impulsive fuzzy differential equations with finite delayed state,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 4, no. 15 , pp. 105–119, 2018, [Online]. Available: https://sid.ir/paper/257290/en

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