An inequality for the spectral radius of an interval matrix

AbstractFor an n × n interval matrix A = (Aij), we say that A is majorized by the point matrix à = (aij) if aij = |Aij| when the jth column of A has the property that there exists a power Am containing in the same jth column at least one interval not degenerated to a point interval, and aij = Aij otherwise. Denoting the generalized spectral radius (in the sense of Daubechies and Lagarias) of A by ϱ(A), and the usual spectral radius of à by ϱ(Ã), it is proved that if A is majorized by à then ϱ(A) ⩽ ϱ(Ã). This inequality sheds light on the asymptotic stability theory of discrete-time linear interval systems