An inequality for the spectral radius of an interval matrix Original Research Article

For an n × n interval matrix A = (Aij), we say that image is majorized by the point matrix à = (aij) if aij = Aij when the jth column of image has the property that there exists a power imagem 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 image by varrho(image), and the usual spectral radius of à by varrho(Ã), it is proved that if image is majorized by à then varrho(A) less-than-or-equals, slant varrho(Ã). This inequality sheds light on the asymptotic stability theory of discrete-time linear interval systems.