New stability criterion of fractional-order impulsive coupled non-autonomous systems on networks

Abstract This paper explores stability of new fractional-order impulsive coupled (FOIC) non-autonomous systems on networks. By utilizing graph theory and structuring individual vertex’s Lyapunov function, a systematic method is present to construct global Lyapunov functions of FOIC systems. By Lyapunov method, a new inequality as well as the graph theory, several new stable principles are derived based on the strongly connected property. Besides, several more general criteria are obtained by utilizing these principles to the FOIC systems, including uniform stability, exponential stability and Mittag-Leffler stability for a kind of FOIC systems. At last, a numerical example is provided to show the effectiveness of our findings.