Eigenvalue clustering in subregions of the complex plane for interval dynamic systems

Abstract

Various sufficient conditions of eigenvalue clustering for interval matrices are presented. The proposed sufficient conditions guarantee that all eigenvalues of the interval matrices lie inside various specified regions in the complex plane. The derived theorems can be applied to both continuous- and discrete-time dynamic interval systems. The dynamical characteristics of a linear system are influenced by the eigenvalue locations of the system. Therefore, by the analysis of eigenvalue clustering, we can understand more properties about interval dynamic systems such as stability margin, performance robustness and so on. Three examples are given to illustrate the applicability of the results.