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

Nicolae Lupa
2020 Mathematics  
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
more » ... ss of difference equations.
doi:10.3390/math8071095 fatcat:lv563jlbwvdklcocax3mbot7ji