Exponentially Stable Periodic Oscillation and Mittag–Leffler Stabilization for Fractional-Order Impulsive Control Neural Networks With Piecewise Caputo Derivatives
研究了具有分段卡普托导数的脉冲分数阶神经网络，证明了其周期振荡的存在唯一性和全局指数稳定性，并提出了脉冲控制下的Mittag-Leffler镇定方法。
It is well known that the conventional fractional-order neural networks (FONNs) cannot generate nonconstant periodic oscillation. For this point, this article discusses a class of impulsive FONNs with piecewise Caputo derivatives (IPFONNs). By using the differential inclusion theory, the existence of the Filippov solutions for a discontinuous IPFONNs is investigated. Furthermore, some decision theorems are established for the existence and uniqueness of the (periodic) solution, global exponential stability, and impulsive control global stabilization to IPFONNs. This article achieves four key issues that were not solved in the previously existing literature: 1) the existence of at least one Filippov solution in a discontinuous IPFONN; 2) the existence and uniqueness of periodic oscillation in a nonautonomous IPFONN; 3) global exponential stability of IPFONNs; and 4) impulsive control global Mittag-Leffler stabilization for FONNs.