Abstract
This paper focuses on the predefined-time synchronization (PTS) of incommensurate fractional-order competitive neural networks (IFCNNs) with bounded or unbounded time-varying delays in the sense of Caputo fractional derivative (CFD). To this end, based on the piecewise Lyapunov function, a novel predefined-time stability theorem (PTST) is presented, where the setting of an adjustable time parameter in the deduced results makes it to be more versatile and more flexible, which refines former studies and can infer a series of new results. Besides, a double-layers predefined-time controller with two different fractional-order integrals is proposed, where the predefined time (PT) is predefined during the control design and can ensure that before a known time. Using this new PTST and some inequality techniques, an effective criteria for ensuring the PTS for two IFCNNs is derived in terms of algebraic inequalities. The PT is set to any positive parameter in the controllers and wholly independent of the initial values. Finally, examples are given to verify the proposed results.
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