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Electrical waves circulating around an obstacle in cardiac tissue are subject to a generic oscillatory instability. In a one-dimensional ring geometry this instability can produce both quasiperiodic and spatiotemporally chaotic oscillations while in a two-dimensional sheet of cardiac tissue it can lead to spiral wave breakup. We present a control scheme to prevent this instability in these two geometries which is based on applying a feedback current at a discrete set of control points during the repolarizing phase of the action potential. The feasibility of this scheme is demonstrated via simulations of a two-variable model of excitable media with restitution and of the Beeler-Reuter model of ventricular action potential.