Abstract This conceptual numerical study explores a possible strategy for control of unstable intrinsic thermoacoustic (ITA) modes. Control of the ITA feedback loop has not been discussed yet. We propose addition of hydrogen fuel as a means of control and investigate the effect of incremental addition to the fuel mixture on the stability of a laminar slit flame using a variety of approaches: first, the ITA frequencies are estimated by a chemical kinetics solver for hydrogen fuel content up to 50% of the total fuel mass flow. Second, we perform DNS for each case and compute the Flame Transfer Function (FTF), from which the ITA mode frequencies and their stability can be estimated. Additionally, for each case the unstable flame is computed to confirm the estimated ITA mode frequencies. Third, an acoustic network model is employed, which uses the FTFs and predicts the stability limits observed by the DNS. Comparison with DNS data features very good agreement and allows to model the impact of hydrogen on the stability of the combustor.