Finite time stability of fractional delay difference systems: A discrete delayed Mittag-Leffler matrix function approach

Abstract

Abstract A discrete delayed Mittag-Leffler matrix function is developed in this paper. Based on this function, an explicit formula of the solution of fractional delay difference system (FDDS) is derived. Furthermore, a criterion on finite time stability (FTS) of FDDS with constant coefficients is obtained by use of this formula. However, it can’t be directly used to investigate the FTS of FDDS with variable coefficients. To overcome this difficulty, a comparison theorem of FDDS is established to obtain a criterion of the FTS of FDDS with variable coefficients. Finally, a numerical example is given to show the effectiveness of the proposed results.