Trajectory Linearization Control is applied to the longitudinal hypersonic scramjet vehicle model under development at the Air Force Research Laboratory. The algorithm is based on Differential Algebraic Spectral Theory which features a time-varying eigenvalue concept and avoids the use of so-called frozen-time eigenvalues which can lead to unreliable results when applied to time-varying dynamics systems. A trajectory linearization control was first designed for a non-linear, affine, rigid-body model using an ...