Finite‐Time Intra‐Layer and Inter‐Layer Synchronization of Fractional‐Order Multi‐Layer Networks With Time‐Varying Delays

ABSTRACT This paper focuses on the finite‐time intra‐layer synchronization (FTALS) and finite‐time inter‐layer synchronization (FTRLS) of fractional‐order multi‐layer networks (FOMLNs) with time‐varying delays. To begin, two forms of continuous control schemes with time‐varying delays are proposed: State feedback control and fractional‐order adaptive control. Following that, based on the finite‐time stability theory and utilizing fractional‐order differential inequalities and other inequality approaches, several new sufficient conditions for intra‐layer synchronization (ALS) and inter‐layer synchronization (RLS) of FOMLNs in finite time are given. Furthermore, the control gains here can be widely selected, and the upper bounds of the settling times for FTALS and FTRLS are explicitly derived in terms of the control gains and network parameters. Lastly, the viability of the theoretical results is demonstrated by two numerical examples.