Systems with Fractional Variable-Order Difference Operator of Convolution Type and Its Stability

In the paper the Grunwald-Letnikov-type linear fractional variable order discrete-time systems are studied. The conditions for stability and instability are formulated. The regions of the systems stability are determined accordingly to locus of eigenvalues of a matrix associated to the considered system. Index Terms--Asymptotic stability; Fractional calculus; Stability analysis; System analysis and design.