Exponential stability of a class of linear time-varying singularly perturbed systems

Abstract

In this paper, the Gauss-Seidel iteration method is used to investigate the exponential stability of a class of linear time-varying singularly perturbed systems. A simple algebraic criterion for exponential stability for all small enough values of singular perturbation parameter ε is obtained. Moreover, an upper bound on the values of ε for which the system preserves exponential stability can be found by solving a set of ε-dependent inequalities.