In this paper, we are concerned with the existence and stability of pullback exponential attractors for a non-autonomous dynamical system. (ⅰ) We propose two new criteria for the discrete dynamical system and continuous one, respectively. (ⅱ) By applying the criteria to the non-autonomous Kirchhoff wave models with structural damping and supercritical nonlinearity we construct a family of pullback exponential attractors which are stable with respect to perturbations.
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