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Unlike the Nyquist criterion, root locus, and many otherstability criteria, the well-known Routh-Hurwitz criterion isusually introduced as a mechanical algorithm and no attempt ismade whatsoever to explain why or how such an algorithm works. Itis widely believed that simple derivations of this importantcriterion are highly requested by the mathematical community. In this paper, we address this problem and provide a simple proof of the Routh-Hurwitz criterion based on two generalizations of an interesting property known in stability theory as theinterlacing property. Within the same context, the singularitiesthat may arise in the Routh-Hurwitz criterion are also dealt with

On the interlacing property and the Routh-Hurwitz criterion