Stability Analysis of Caputo-Like Discrete Fractional Systems

Abstract

This study investigates stability of Caputo delta fractional difference equations. Solutions' monotonicity and asymptotic stability of a linear fractional difference equation are discussed. A stability theorem for a discrete fractional Lyapunov direct method is proved. Furthermore, an inequality is extended from the continuous case and a sufficient condition is given. Some linear, nonlinear and time varying examples are illustrated and the results show wide prospects of the stability theorems in fractional control systems of discrete time. (C) 2017 Elsevier B.V. All rights reserved.