A sufficient condition for matrix stability

Abstract

An n by n complex matri x A is said to be pos itive stable if Re (A) > 0 for each e igenvalue A of A. If A sati sfies both of the followin g two conditions, the n A is positive stable: (1) for each k = 1, .. . , n , the real part of the sum of the k by k princ ipal minors of A is positive ; and (2) the minimum of the rea l parts of the e igenvalues of A is it se lf an eigenvalue of A. Special cases inc lude hermiti a n positive d e fi nite matrices and M-matrices.