Further Results on Diagonally Invariant Exponential Stability of Switching Linear Systems

Abstract

The concept of diagonally invariant exponential stability (DIES) was originally introduced for single-model linear systems and subsequently expanded in the study of linear systems with interval-type uncertainties and linear systems with arbitrary switching. The results presented in this article refer to new approaches to DIES characterization for arbitrary switching systems, which exploit mathematical tools completely different from earlier work. The previous papers are based on the properties of matrix norms and measures applied to the constituent matrices defining the switching system, while the present paper uses the eigenvalues and eigenvectors of the column and row representatives built for a set of matrices derived from the constituent matrices of the switching system. The applicability of previous and new results, respectively, is illustrated by case studies (in both continuous- and discrete-time) that lead to relevant comparisons between the two classes of analysis methods.