On the poles of two‐time‐scale systems

Abstract

In this note, the authors will study how the poles of a linear time-invariant singularly perturbed system are varied versus singular parameter ε, where the poles of the slow and fast subsystems are assumed to be placed in the prescribed regions. An explicit ε $\ \varepsilon $ bound is derived such that the poles of the original full order system remain in these regions. Finally, two examples are illustrated to show the applications of the proposed results.