Linearized stability analysis methodologies that are applicable to large scale, multiphysics problems are presented in this paper. Two classes of closely related algorithms based on a partial Floquet and on an autoregressive approach, respectively, are presented in common framework that underlines their similarity and their relationship to other methods. The robustness of the proposed approach is improved by using optimized signals that are derived from the proper orthogonal modes of the system. Finally, a signal synthesis procedure based on the identified frequencies and damping rates is shown to be an important tool for assessing the accuracy of the identified parameters; furthermore, it provides a means of resolving the frequency indeterminacy associated with the eigenvalues of the transition matrix for periodic systems. The proposed approaches are computationally inexpensive and consist of purely post processing steps that can be used with any multiphysics computational tool or with experimental data. Unlike classical stability analysis methodologies, it does not require the linearization of the equations of motion of the system.