A New Approach on Datko–Zabczyk Method for Nonuniform Exponential Stability

Nicolae Lupa
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Nicolae Lupa: Department of Mathematics, Politehnica University of Timişoara, Piaţa Victoriei 2, 300006 Timişoara, Romania

Mathematics, 2020, vol. 8, issue 7, 1-10

Abstract: We provide a sequence of projections on the linear space of all sequences and connect the existence of nonuniform exponential stability to the restrictions of these projections on a class of Banach sequence spaces defined by a discrete dynamics. As a consequence, we obtain a Datko–Zabczyk type characterization of nonuniform exponential stability. We develop our analysis without any assumption on the invertibility of the dynamics, thus our results are applicable to a large class of difference equations.

Keywords: discrete dynamics; nonuniform exponential stability; Banach sequence spaces; Datko–Zabczyk theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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