Cheyne-Stokes respiration (CSR) foretells deleterious outcomes in patients with heart failure. Currently, the size of therapeutic intervention is not guided by the patient's underlying pathophysiology. In theory, the intervention needed to resolve CSR, as a control system instability (loop gain >1), can be predicted knowing the baseline loop gain and how much it falls with therapy. In 12 patients with heart failure, we administered an inspiratory carbon dioxide fraction of 1-3% during CSR (n=95 interventions) as a means to reduce loop gain. We estimated the loop gain on therapy (LGtherapy), using the baseline loop gain (using hyperpnoea length/cycle length) and its expected reduction (18% per 1% inspired carbon dioxide), and tested the specific hypothesis that LGtherapy predicts CSR persistence (LGtherapy >1) versus resolution (LGtherapy <1). As predicted, when LGtherapy >1.0, CSR continued during therapy in 23 out of 25 (92%) trials. A borderline loop gain zone (0.8<LGtherapy<1) yielded an unpredictable outcome, while LGtherapy <0.8 consistently yielded CSR resolution (37 out of 37 trials). A threshold of LGtherapy=0.9 determined outcome in 76 out of 95 (80%) trials. We establish proof-of-concept that control theory provides predictive insight into CSR resolution in heart failure. Thus, we now have a means to calculate the size of interventions needed to ameliorate CSR on a patient-by-patient basis.