A feedback control strategy is developed for mitigating combustion instabilities using a Helmholtz resonator with an oscillating volume. This is based on the fact that the frequency at which the resonator provides maximum damping can be controlled by oscillating its cavity volume. For this, two algorithms are developed. One is a real-time plane-wave decomposition algorithm; the other is a finite impulse response filter, its coefficients being optimized by the least-mean-square method but with a variable step size. The filter uses the decomposed incident wave to determine the optimum actuation signal. The performance of the control strategy, carried out with off-line system identification, is evaluated via a numerical model of an unstable combustion system with a dominant longitudinal mode. It is successfully demonstrated that the control strategy is more robust and capable of stabilizing the combustion system at a faster rate than that of conventional filters with fixed step size.