To guarantee safety and stability of robotic and telerobotic rehabilitation systems, new mathematical frameworks and stabilizing controllers have been developed in our team based on (a) the Small-Gain approach and (b) Strong Passivity theory. System stability and force fidelity are analyzed in the presence of nonpassive, nonlinear, and nonautonomous behavior of the terminals (including the dynamical features of the therapist and the patient) together with time-varying communication delays for the case of remote and cloud-based therapy. Several practical considerations have been taken into account to match the clinical needs and minimize the implementation cost. The effectiveness of the approach has been tested through extensive user studies and statistical evaluations. The stability framework considers “variability” in the biomechanical capability of the human upper-limb in absorbing interactive forces and energies. The goal is to maximize the transparency and performance of the system. For this purpose, the Grasp-based Passivity Signature (GPS) map was proposed and studied. The GPS map considers variability in the geometry of the interaction and the grasp condition to interpolate the Excess of Passivity (EOP) of the patient’s hand in every time stamp.