Finite-Time Stability of Fractional Time Delay System

Abstract

In this study, some basic results of the stability criteria of fractional order systems with time-delay as well as free-delay are presented. Particularly, they are obtained and presented sufficient conditions for finite time stability for (non)linear (non)homogeneous as well as perturbed fractional order time-delay systems. Several stability criteria for this class of fractional order systems are proposed using a recently suggested generalized Gronwall inequality as well as “classical” Bellman-Gronwall inequality. Some conclusions for stability are similar to those of classical integer-order differential equations. Lastly, numerical examples are given to illustrate the validity of the proposed procedure.