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In this paper we introduce some stability criteria of nonlinear hybrid systems with time delay described by impulsive hybrid fuzzy system of differential equations. Firstly, a comparison principle for fuzzy differential system based on a notion of upper quasi-monotone nondecreasing is presented. Here, for stability analysis of fuzzy dynamical systems, vector Lyapunov-like functions are defined. Then, by using these functions together with the new comparison theorem, we will get results for some concepts of stability (eventual stability, asymptotic stability, strong stability and uniform stability) for impulsive hybrid fuzzy delay differential systems. Furthermore, theorems for practical stability in terms of two measures are introduced and are proved. Finally, an illustrating example for stability checking of a differential system with fuzziness and time delay is given. Then, by introducing an applied example in Pharmacokinetics, we bridge theoretical concepts to the application of research in real world.

Stability analysis of nonlinear hybrid delayed systems described by impulsive fuzzy differential equations