Robustness of eigenvalue clustering in various regions of the complex plane for perturbed systems

Abstract

Sufficient conditions of robust eigenvalue clustering for perturbed systems are presented. If all the eigenvalues of the nominal system are located in a specified region of the complex plane then the proposed sufficient conditions guarantee that all the eigenvalues of the perturbed system remain inside the same region. The characteristics of a linear dynamical system are influenced by the eigenvalue locations. Therefore, through the study of eigenvalue clustering, more features about perturbed systems, such as stability margin, performance robustness and so on, can be investigated. It is emphasized that the proposed perturbation bounds for robust eigenvalue clustering in a specified region can be applied to both continuous- and discrete-time systems. Three illustrative examples are given to show the applicability of the proposed theorems.