Finite-time stability of perturbed fractional-order systems with multiple time-varying delays

Abstract

The theory and applications of fractional calculus had a considerable progress in recent decades. Fractional calculus attracts much attention since it plays an important role in many fields of science and engineering. Dynamical systems and control are one of the most active areas in applications of fractional calculus. Especially, the study of stability and stabilization of fractionalorder systems is very important. Time-delay systems are important class of dynamical systems, since, in real world systems, delay is present everywhere. Considerable attention has been paid to fractional dynamical systems with time delay. In this paper, a stability test procedure is suggested for perturbed nonlinear nonhomogeneous fractional-order systems with time-varying delays. Some basic results from the area of finite-time stability are extended to this class of fractionalorder time-delay systems given in state-space form. Sufficient conditions for finite-time stability are derived using recently obtained generalized Gronwall inequality. Finally, a numerical example is given to demonstrate the effectiveness of the presented analytical approaches.