Global stability problem for feedback control systems of impulsive fractional differential equations on networks

This paper studies a novel class of feedback control systems of impulsive fractional differential equations on networks (FCSIFDENs). By combining some graph theory and the Lyapunov method, we provide a systematic method for constructing a global Lyapunov function for FCSIFDENs. Consequently, a new global asymptotic stability principle and a new global Mittag-Leffler stability principle, which have a close relation to the topology property of the network, are given. Finally, numerical examples are given to demonstrate the effectiveness of the theoretical results.