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

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