Cheban, David N.2020-02-202020-02-202001-01-03Cheban, D. N. (2001). Uniform exponential stability of linear periodic systems in a Banach space. <i>Electronic Journal of Differential Equations, 2001</i>(03), pp. 1-12.1072-6691https://hdl.handle.net/10877/9321This article is devoted to the study of linear periodic dynamical systems, possessing the property of uniform exponential stability. It is proved that if the Cauchy operator of these systems possesses a certain compactness property, then the asymptotic stability implies the uniform exponential stability. We also show applications to different classes of linear evolution equations, such as ordinary linear differential equations in the space of Banach, retarded and neutral functional differential equations, some classes of evolution partial differential equations.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalNon-autonomous linear dynamical systemsGlobal attractorsPeriodic systemsExponential stabilityAsymptotically compact systemsEquations on Banach spacesArticle