Exploring a new discrete delayed Mittag–Leffler matrix function to investigate finite‐time stability of Riemann–Liouville fractional‐order delay difference systems
Feifei Du, Jun‐Guo Lu
Abstract
In this paper, firstly, a new discrete delayed Mittag–Leffler matrix function is introduced, which generalizes the existing discrete delayed exponential matrix function. Secondly, based on it, the explicit formula of the solution of homogeneous Riemann–Liouville (RL) fractional‐order delay difference system is obtained. Thirdly, the explicit formulas of the solutions of nonhomogeneous RL fractional‐order delay difference systems are also derived in terms of the superposition principle and the new discrete delayed Mittag–Leffler matrix function. Furthermore, a finite‐time stability (FTS) criterion of nonhomogeneous RL fractional‐order delay difference system is given using the properties of the new discrete delayed Mittag–Leffler matrix function. Finally, three examples are presented to demonstrate the effectiveness of the proposed theorems.