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Unlike the observer design for a conventional system, designing observer for a fractionalorder one is a challenging work due to the different operational properties between the traditional calculus and the fractional calculus. In this paper, two observers for fractional-order neural networks (FONNs) with and without parametric uncertainties are designed, respectively. By using fractional stability criteria, it is shown that the observe errors converge to an arbitrary small region eventually. By using a new sliding term in the synchronization controller desgin, the proposed observers have good robustness. Simulation studies are given to verify the theoretical derivation at last. INDEX TERMS Observer design; fractional-order neural network; chaotic system; parametric uncertainty.

The finite-time synchronization of fractional-order coupled neural networks (FCNNs) is investigated in this paper. A model with multiple output coupling weights and external disturbances is considered, which is a generalized form of frequently used FCNNs with state coupling. In addition, a criterion that can be used to judge whether fractional-order systems are practically finite-time stable is proposed. Furthermore, an adaptive controller is synthesized to ensure the practical finite-time synchronization of FCNNs based on this criterion and the linear matrix inequality technique, and the upper bound of the setting time can be estimated. Finally, a simulation example is provided to illustrate the plausibility of the obtained results.

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