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A new approach via the real structured singular value analysis is proposed to test for the absolute stability of multivariable Lur'e systems. The approach presented in this paper holds for any sector-bounded, slope-restricted or secant-restricted nonlinearities commonly encountered in Lur'e systems. In addition, not only does it yield sharp stability bound, but also it removes some essential assumptions made in other existing results. Moreover, our algorithm can be easily and systematically extended to some more involved configurations, such as a Lur'e type system involved in two or more nonlinearities in different locations, or a multilayer recurrent neural network.