Finite-time stability of impulsive fractional-order systems with time-delay

• Sufficient conditions for the FTS of the proposed systems are established.
• Relations between the estimated time and the impulses are deduced.
• Calculation methods of the estimated time of FTS are illustrated.

In this paper, a class of impulsive fractional-order systems with time-delay is investigated. Sufficient conditions for the finite-time stability(FTS) of impulsive fractional-order systems with time-delay are established by the generalized Gronwall’s inequality. It shows that the FTS of such systems depends on the frequency and amplitude of the impulses. Examples are given to illustrate the results.