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

Author

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  • Nicolae Lupa

    (Department of Mathematics, Politehnica University of Timişoara, Piaţa Victoriei 2, 300006 Timişoara, Romania)

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.

Suggested Citation

  • Nicolae Lupa, 2020. "A New Approach on Datko–Zabczyk Method for Nonuniform Exponential Stability," Mathematics, MDPI, vol. 8(7), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1095-:d:380275
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