Stability and stabilization of short memory fractional differential equations with delayed impulses

Abstract

This paper concentrates on the stability and stabilization of short memory fractional differential equations with delayed impulses. The sufficient conditions for asymptotic stability of short memory fractional differential equations with two kinds of delayed impulses are derived, respectively. The results show that the delayed impulses in short memory fractional differential equations exhibit double effects on system performance. For an unstable system, one can stabilize the system by inputting delays in impulses; for a stable system, the stability would be destroyed if the delays were too long. Further, a class of fractional chaotic systems is presented to test the validity of the established theoretical results, some criteria for impulsive synchronization of fractional chaotic systems are derived, and the corresponding impulsive controllers are designed. Finally, a fractional Chua chaotic oscillator is presented to illustrate the practicability of the established impulsive controllers.