Diagonalization and stability of multi-time-scale singularly perturbed linear systems

摘要

In this paper, an alternate approach to the method of asymptotic expansions for the study of a singularly perturbed, linear system with multiparameters and multi-time scales, is developed. The method consists of developing a linear, nonsingular transformation that enables to decouple the original system completely. This process of diagonalization thus provides a very simple and suitable tool to investigate (i) the stability analysis and (ii) approximations of solutions of original system in terms of the overall reduced system and the corresponding boundary layer systems.