To effectively control thermoacoustic instability represented as high-amplitude oscillations， the coupling control method for Rijke tube based on Lyapunov stability principles is explored. The key coefficient matrices are obtained through linearization and matrix control formulation of the coupled system. Predictions of the control parameter range strategy for achieving amplitude death of the coupling control system are based on the real part of the eigenvalues. The research demonstrates that the maximum transient energy growth rate is closely associated with the minimum real part of the eigenvalues， validating the efficacy of the coupling control strategy based on the Lyapunov stability principles. A larger minimum real part value results in a faster decay rate of transient energy， but employing a coupling system with the ratio of heat intensity larger than one leads to a transient energy growth.