A note on the nonuniform exponential stability and dichotomy for nonautonomous difference equations

In their recent result Hu and Mitsui proved that any exponentially stable nonautonomous linear difference equation can be reduced via suitable change of variables to equivalent linear difference equations whose coefficient matrices have spectral norm which is less then 1. In the present paper, we pr...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 552; pp. 105 - 126
Main Author Dragicevic, Davor
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.09.2018
American Elsevier Company, Inc
Subjects
Dichotomies
Difference equations
Differential equations
Linear algebra
Mathematical analysis
Matrix
Matrix methods
Nonautonomous difference equations
Nonuniform exponential stability
Numerical analysis
Theoretical mathematics
Nonuniform exponential stability
Nonautonomous difference equations
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Summary:In their recent result Hu and Mitsui proved that any exponentially stable nonautonomous linear difference equation can be reduced via suitable change of variables to equivalent linear difference equations whose coefficient matrices have spectral norm which is less then 1. In the present paper, we prove that this statement holds under weaker assumption that the nonautonomous linear difference equation is (strongly) nonuniformly exponentially stable. Moreover, we also establish corresponding results in the case of strong nonuniform exponential dichotomies.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2018.04.018