Stability criterion for a sampled-data system with digital controller

A sampled-data system consisting of a continuous LTI (linear time-invariant) plant and a digital implementation of an analog LTI strictly proper controller with a strictly proper continous-time prefilter in the output feedback loop is considered. A quantitative sufficient stability condition is formulated. This condition shows how to determine the interval of the sampling frequency inside of which asymptotic stability of the continuous-time closed-loop counterpart of the sampled-data system implies exponential stability of the hybrid system and therefore I_p-stability of the latter