Conditions for scale-based decompositions in singularly perturbed systems (Q1101048)

From the authors abstract: ``... consider the linear systems of the form \(\dot x=A(\epsilon)x\), with A(\(\epsilon)\) analytic at 0, nonsingular for \(\epsilon \in (0,\epsilon_ 0]\), and singular at \(\epsilon =0..\). Using ideas from an algebraic approach that we have developed for the study of singularly perturbed systems, we show (among other results): that the Smith decomposition of \(A(\epsilon)\) permits transformation to a form in which the scales become explicit and the computations become transparent and simple...''