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.