An improved result for the stability of interconnected systems based on a new Gersgorin-type criterion

Abstract

In this short paper, a new Gersgorin-type criterion for eigenvalue inclusion sets is used to derive a new sufficient condition for the positive definiteness of real symmetric matrices. The result is less conservative than the classic strict diagonal dominance criterion imposed by Gersgorin's Theorem. We show that this result can be applied to various classes of interconnected systems, including systems consisting of subsystems with linear and nonlinear interconnection terms. Numerical examples as well as the intuition behind the derived results are also provided.