This work demonstrates real-time control of cardiac alternans in the extracted rabbit heart and provides an analysis of the control methodology applied in the case of a one dimensional (1D) cable of cardiac cells. The real-time applied control is realized through feedback by proportional perturbation of a basic pacing cycle length (PCL). Measurements of the electric wave propagation are obtained by optical mapping of fluorescent dye from the surface of the heart and fed back in the custom designed software that provides the control input signal, which perturbs the basic pacing cycle length. In addition, a novel pacing protocol that avoids conduction block is applied. A complementary numerical analysis to the experiment is given by dimensionally reduced ionic model of the 1D cable of cardiac cells under the self-referencing feedback protocol, which is identical to the one applied in the experimental study. In addition, the amplitude of alternans linear parabolic PDE with gain full state feedback control associated with the ionic 1D cardiac cell cable model is explored and analyzed. The analysis of stabilization of the amplitude of alternans PDE is in an agreement with experimental results obtained and numerical results produced by the ionic 1D cable of cardiac cells model.