The equivalence of time-scale decomposition techniques used in the analysis and design of linear systems

Linear system models can be decomposed into reduced-order ‘ fast’ and ‘ slow ’ subsystems using ‘ spectrum separating ’ solutions to dual Riccati type equations. Eigenspace power iterations provide globally convergent iterative schemes for obtaining these solutions. From this basis, an equivalence of previous decomposition techniques is then achieved including the classic two-time-scale asymptotic series decomposition of singularly perturbed systems. The result is a unified theory for the decomposition of time scales in linear systems applicable to both continuous and discrete time models.