Gershgorin disk theorem in complex interval matrices

Abstract

In this article, the Gershgorin disk theorem in complex interval matrices is proposed for enclosing interval eigenvalues. This is a non-iterative method for finding eigenvalue bounds for both real and imaginary parts. Moreover, we are able to find gaps between the clusters of interval eigenvalues and have compared the results with the previous theorems for interval eigenvalue bounds for complex interval matrices. These results can be decisive for checking Hurwitz and Schur stability of complex interval matrices that appear in uncertain dynamical systems. Further bounds obtained from the present formulae can be considered as the initial bounds for iterative methods.

Keywords

• complex interval matrices
• gershgorin disk theorem
• interval eigenvalues
• eigenvalue bounds.