We propose a theoretical framework and an automated algorithm for the construction of a parameterized reduced-order model of a general LTI system from its sampled input-output responses. The model is cast as a parameterized rational function in Generalized Sanathanan-Koerner form, which allows for implicit parameterization of the model poles. Our main result is the guaranteed enforcement of uniform stability of the model in the parameter space through a sufficient condition, which requires the (strict) positive realness of the denominator subsystem. This condition is enforced through adaptive constraints during the model construction loop. Several applications to the field of Electronic Design Automation are presented.