The concept of basic systems as systems with a transfer function in the form of an in- verse characteristic polynomial of the system is introduced. For these basic systems, we obtain spectral decompositions of energy-based stability metrics from their state-space representations in canonical forms, including Jordan, modal, controllability, and observability. We present ex- plicit formulas for the spectral decomposition of the squared H2-norm, specifically for the case where the transfer function possesses repeated poles. Furthermore, we develop efficient recur- sive algorithms to compute the spectral decompositions of the inverse matrices of gramians of continuous dynamical systems based on the repeated spectra of the original dynamics matri- ces. Spectral decompositions of energy stability metrics are obtained in the form of spectral decomposition of the square H2-norm of the transfer function of the base system for the case of its simple and multiple roots. A new approach to analyzing the stability of linear systems based on an enhanced Routh–Hurwitz stability criterion is proposed, which includes forming Routh tables and Xiao matrices, computing the spectrum of the dynamics matrix, comput- ing spectral decompositions of energy-based metrics, and jointly applying the Routh–Hurwitz stability criterion and the criterion of boundedness of energy-based stability metrics of basic systems. Finally, we conclude with practical recommendations for applying these theoretical and algorithmic results in systems analysis and design.