Asymptotic Stabilization Control of Fractional-Order Memristor-Based Neural Networks System via Combining Vector Lyapunov Function With <i>M</i>-Matrix
Zhe Zhang, Yaonan Wang, Jing Zhang, Hui Zhang, Zhaoyang Ai, Kan Liu, Feng Liu
Abstract
This article examines a new measure of combining the vector Lyapunov function with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}$ </tex-math></inline-formula> -matrix for settling the asymptotic stabilization control of fractional-order memristor-based neural networks system (FOMBNNS) has large delays in various dimensional forms. Some new stability and stabilization criteria are deduced. First, the vector Lyapunov function and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}$ </tex-math></inline-formula> -matrix are imported for investigating stabilization control for the above system. Then, we solve the problem for a special type of situation that the activation functions no longer consider Lipschitz parameters via the new method. Finally, four numerical examples from different kinds of situations are simulated for expounding the validity of the novel asymptotic stability and stabilization criteria. Compared with the methods mentioned in the current references, the proposed asymptotic stability and stabilization criteria in this article have strong generality and universality. They can be applied not only to the most common feedback control, accordingly, the feedback control law based on which they are designed but also to all fractional-order parameters from 0 to 1. In addition, the new method has lower conservativeness and fewer constraints. Moreover, the new stability and stabilization criteria can also overcome the difficulty in dealing with the above system owning large delays.