Asymptotic Stability and Synchronization of Fractional-Order Neural Networks With Unbounded Time-Varying Delays
Fanghai Zhang, Zhigang Zeng · IEEE Transactions on Systems Man and Cybernetics Systems · 2019
This article deals with the asymptotic stability and synchronization of fractional-order neural networks (FONNs) with unbounded time-varying delays, in which FONNs can be the general nonlinear system. First, the existence of the equilibrium point of the nonlinear system is obtained, and the μ-type stability of fractional-order nonlinear systems is proved by the analytical method. Second, several sufficient conditions are derived to guarantee the μ-type stability of FONNs by taking easily implemented parameters. Moreover, the μ-type synchronization of drive-response systems is established by designing the linear controller. Especially, μ-type stability is the general stability, including Mittag-Leffler stability and power-stability, which is the extension of the Mittag-Leffler stability of FONNs. Finally, two numerical examples are presented to show the effectiveness of the results.