Asymptotic Stability Analysis and Stabilization Control for General Fractional-Order Neural Networks via an Unified Lyapunov Function
Zhe Zhang, Yaonan Wang, Zhiqiang Miao, Yiming Jiang, Yun Feng
Abstract
In this study, we propose a novel unified specific Lyapunov function for fractional-order neural networks (FONNs) that comprises two asymptotic stabilization criteria. Initially, we deduce a specific Lyapunov function that applies to all FONNs. This function does not limit the signs of the state variables and exhibits low conservativeness. Subsequently, based on this explicit Lyapunov function, we design two new control strategies. Additionally, by combining the vector Lyapunov function with the M-matrix method, we derive two corresponding asymptotic stabilization criteria to obtain the scopes of the two control laws. Ultimately, we verify the effectiveness of the two control strategies based on the new unified specific Lyapunov function through numerical simulations. Contrary to the simulations of other references, we also consider various scenarios that more closely resemble authentic situations, including high dimensions, larger time delays, a greater number of initial values, and multiple fractional orders.