Stability Analysis of Matrices and Single-Parameter Matrix Families on Special Regions

This paper proposes an efficient method for determining the D-stability of matrices using Kelley’s cutting-plane method. The study examines the D-stability of matrices in symmetric regions of the complex plane, defined by quadratic matrix inequalities (QMI) and polynomial functions. Using Kelley’s cutting-plane method, we present an iterative algorithm for determining the D-stability of a given matrix. Further, the robustness of single-parameter matrix families is analyzed, and a method is proposed for considering their D-stability. Through examples, we indicate the possible applicability of the proposed approach in addressing stability problems in linear systems.