Absolute stability of a reduced order thermo-acoustic model with non-homogeneous wave speed

Through application of the Kalman-Yakubovich- Popov lemma, we present an analysis of absolute stability of a Galerkin-truncated reduced order thermo-acoustic PDE model with uncertain nonlinear feedback and non-homogeneous wave-speed. The analysis is applicable to Galerkin-truncations with arbitrarily high dimension and therefore the analysis is applicable to investigating the stability properties of high- order modes of the system. The effects of nonlinear coupling on the stability of the high-order system modes are revealed. This work is a first step toward the analysis of infinite- dimensional stability of the nonlinear system with arbitrary non-homogeneous parameters.