An inequality for the spectral radius of an interval matrix (Q1386494)

The main result of this paper says that for each square interval matrix \({\mathbb A}\) a real matrix \(A\) with the property \[ \rho({\mathbb A})\leq\rho(A) \] can be constructed, where \(\rho\) on the right-hand side stands for the spectral radius whereas on the left-hand one it denotes the generalized spectral radius in the sense of \textit{I. Daubechies} and \textit{J. C. Lagarias} [Linear Algebra Appl. 161, 227-263 (1992; Zbl 0746.15015)]. Further it is proved that \[ \rho({\mathbb A})=\rho(\text{ext} {\mathbb A}), \] where \(\text{ext} {\mathbb A}\) is the set of vertices of \({\mathbb A}\). Application of these results to checking asymptotic stability of discrete time-varying linear systems is considered.