Complementary results on the stability bounds of singularly perturbed systems

In this note, we will provide a new systematic approach to characterize and compute the stability bound of a singularly perturbed linear system. The approach is based on the feedback system representation of an additional matrix perturbation problem. The idea is to change the stability bound problem to the stability problem of an underlying feedback system. This approach allows multiple choices in formulating the underlying feedback system and thus has the potential of characterizing and computing the stability bound in a number of different ways. By formulating two kinds of different feedback systems, some existing and new results on the stability bounds are derived based on the feedback system approach. The new results complement the existing frequency-domain based stability criteria and make the frequency-domain technique more applicable and useful to the stability bound problem. An example is provided to show the new stability criterion is effective and useful in determining the stability bound.