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This thesis gives a study of an aspect of asymptotic stability
theory of matrices. Using the notions of the asymptotic
stability (in the sense of Lyapunov), we prove an asymptotic
stability theorem for matrices. By making use of this stability
theorem, we give a new proof of the recent conjecture
byDaubechies-Lagarias (1992). By inducing the notion of
majorant, we give a characterization of the simultaneous Schur
stability for a familily ofinterval matrices. From this
characterization, an inequality for spectral radii is obtained.
As an application of this inequality, we introduce
efficientconditions for the stability of linear interval
systems.
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