Although passivity has been proven to be quite useful, it excludes a majority of dynamic systems in applications, and typically, the property cannot be preserved through discretization. To overcome these shortcomings, the class of passivity-short (PS) systems is investigated in this article, and canonical forms are derived in both continuous-time and discrete-time domains. Explicit conditions are found to guarantee the PS property through discretizing PS/non-PS systems and, for those that do not satisfy the conditions, two designs of output feedback controls are presented to make sampled-data systems PS, regardless of the PS property of original continuous-time systems. One of the designs is in the discrete-time domain, and the other is in the continuous-time domain. The control design to ensure the PS property in the continuous-time domain is also developed. These results provide a full description of PS systems in both domains as well as their relationship through discretization.