An inequality for the spectral radius of an interval matrix

✍ Scribed by Mau-hsiang Shih; Yung-yih Lur; Chin-tzong Pang

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 389 KB
• Volume: 274
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)00238-3

✦ Synopsis

For an n X n interval matrix ~2 = ( Aij), we say that d is wuzjorized by the point matrix ti = (aij) if aij = 1 Aijl when the jth column of S' has the property that there exists a power P containing in the same jth column at least one interval not degenerated to a point interval, and ai1 = Aij otherwise. Denoting the generalized spectral radius (in the-sense of Daubechies and Lagarias) of S' by p(d), and the_ usual spectral radius of ti by p(M), it is proved that if .& is majorized by S? then p(M) < p(.%$ This inequality sheds light on the asymptotic stability theorv of discrete-time linear interval systems.