In this paper, two new control methods based on a Lyapunov-like function and a vector Lyapunov function separately were put forward to solve the asymptotic stabilization problem of general fractional-order nonlinear systems with multiple time delays. First, we deduced a new asymptotic stabilization control criterion based on a Lyapunov-like function after discussing the asymptotic stability criterion of general fractional-order nonlinear systems. Moreover, to address the problem of multiple time delays of the nonlinear system, we derived another asymptotic stabilization control criterion based on a vector Lyapunov function and an M-matrix via the new controller. Finally, the feasibility and effectiveness of the proposed controllers were verified by several common fractional-order nonlinear systems.

提出了分别基于类Lyapunov函数和向量Lyapunov函数的两种新的控制方法，以解决具有多个时滞的一般分数阶非线性系统的渐近稳定问题。首先，在讨论了一般分数阶非线性系统的渐近稳定准则后，我们基于类Lyapunov函数推导了新的渐近稳定控制准则。此外，为解决非线性系统的多个时滞问题，我们通过新控制器基于矢量Lyapunov函数和M-矩阵推导了另一种渐近稳定控制准则。最后，通过几种常见的分数阶非线性系统验证了所提出控制器的可行性和有效性。