On stability of nonlinear nonautonomous discrete fractional Caputo systems

Conditions to establish Mittag-Leffler stability of solutions for nonlinear nonautonomous discrete Caputo-like fractional systems just from the linear associated system is shown. Mittag-Leffler stability for linear systems is tackled pointing out properties the matrix must satisfy. Additionally features on solutions for linear systems are included in order to establish the equivalence between uniform asymptotical stability and exponential stability. Converse-like-Lyapunov Theorem is developed and a particular result to show Mittag-Leffler stability from a condition on a linear part of the full system is worked. (C) 2020 Elsevier Inc. All rights reserved.