On stability of linear discrete-time fractional systems with variable order and distributed delay

This paper studies discrete-time fractional systems described by the Grünwald-Letnikov-convolution type difference operator, with a particular focus on variable-order cases and systems incorporating infinite distributed delays. Due to the convolution nature of this operator, the Z-transform is employed as a powerful tool for evaluating stability. The work addresses the stability of solutions for linear systems, providing conditions for both stability and instability. Regions of stability are characterized in terms of the eigenvalue loci of an associated system matrix, and illustrative examples are provided.