Asymptotic stability and generalized Gelfand spectral radius formula
نویسندگان
چکیده
منابع مشابه
On explicit a priori estimates of the joint spectral radius by the generalized Gelfand formula
In various problems of control theory, non-autonomous and multivalued dynamical systems, wavelet theory and other fields of mathematics information about the rate of growth of matrix products with factors taken from some matrix set plays a key role. One of the most prominent quantities characterizing the exponential rate of growth of matrix products is the so-called joint or generalized spectra...
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The famous Gelfand formula ρ(A) = lim supn→∞ ‖A ‖ for the spectral radius of a matrix is of great importance in various mathematical constructions. Unfortunately, the range of applicability of this formula is substantially restricted by a lack of estimates for the rate of convergence of the quantities ‖A‖ to ρ(A). In the paper this deficiency is made up to some extent. By using the Bochi inequa...
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The generalized spectral radius, also known under the name of joint spectral radius, or (after taking logarithms) maximal Lyapunov exponent of a discrete inclusion is examined. We present a new proof for a result of Barabanov, which states that for irreducible sets of matrices an extremal norm always exists. This approach lends itself easily to the analysis of further properties of the generali...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00592-7