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This paper is concerned with the problem of observer design for switched recurrent neural networks with time-varying delay. The attention is focused on designing the full-order observers that guarantee the global exponential stability of the error dynamic system. Based on the average dwell time approach and the free-weighting matrix technique, delay-dependent sufficient conditions are developed for the solvability of such problem and formulated as linear matrix inequalities. The error-state decay estimate is also given. Then, the stability analysis problem for the switched recurrent neural networks can be covered as a special case of our results. Finally, four illustrative examples are provided to demonstrate the effectiveness and the superiority of the proposed methods.