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This brief discusses the stability and stabilization of a class of fractional-order nonlinear systems with Caputo derivative. On the basis of the stability theory of fractional-order linear differential equation, Mittag-Leffler function, Laplace transform, and the Gronwall inequality, two sufficient conditions are derived for the asymptotical stability of a class of fractional-order nonlinear systems with fractional-order α : 0 < α ≤ 1 and 1 < α < 2, respectively. Then, two sufficient conditions for asymptotical stabilization of such fractional-order systems are obtained, in which feedback gains could be ensured by the pole placement technique. Finally, some numerical examples are provided to show the validity and feasibility of the proposed method.

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Abstract:The synchronization problem is studied in this paper for a class of fractional-order chaotic neural networks. By using the Mittag-Leffler function, M-matrix and linear feedback control, a sufficient condition is developed ensuring the synchronization of such neural models with the Caputo fractional derivatives. The synchronization condition is easy to verify, implement and only relies on system structure. Furthermore, the theoretical results are applied to a typical fractional-order chaotic Hopfield neural network, and numerical simulation demonstrates the effectiveness and feasibility of the proposed method.

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