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In this paper, the robust stability of a class of switched Hopfield neural systems with discrete and distributed time-varying delays is considered. The parameter uncertainties are assumed to be norm bounded. Firstly, sufficient conditions for exponential stability criteria of switched Hopfield neural systems are investigated for arbitrary switching signal with average dwell time; Secondly, some criteria are given to guarantee the uncertain switched Hopfield neural systems to be exponential stable for all admissible parametric uncertainties. These results are obtained based on Lyapunov's stability analysis via Krasovsky-Lyapunov's functionals and the related stability study is performed to obtain delay-dependent results. These conditions are expressed in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed theory.