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If the ROC contains the unit circle (i.e., |z| = 1) then the system is stable.
It was later dubbed "the z-transform" by Ragazzini and Zadeh in the sampled-data control group at Columbia University in 1952.
The idea contained within the Z-transform is also known in mathematical literature as the method of generating functions which can be traced back as early as 1730 when it was introduced by de Moivre in conjunction with probability theory.
The following substitution is used: from the Z-domain to the Laplace domain.
Through the bilinear transformation, the complex s-plane (of the Laplace transform) is mapped to the complex z-plane (of the z-transform).
This extends to cases with multiple poles: the ROC will never contain poles.