In this study, a novel unified stability criterion is first proposed for general fractional-order systems with time delay when the fractional order is from 0 to 1. Such a new unified criterion has the advantage of having an initiative link with the fractional orders. A further advantage is that the corresponding asymptotic stability theorem, derived from the proposed criterion used to analyze the asymptotic stability, is only slightly affected by the change of the fractional order. In addition, the unified stability criterion is applied to general multi-dimensional nonlinear fractional-order systems with time delays, the corresponding asymptotic stability criterion is applied by combining the vector Lyapunov function with the M-matrix method. Compared with the traditional stability criterion, the unified stability criterion is slightly influenced by the changing fractional order and large time delays. The reliability and effectiveness of the novel uniform stability criterion were verified through three representative examples.

本研究首次针对分数阶从0到1时滞的一般分数阶系统提出了一种新的统一稳定性判据。这种新的统一判据具有与分数阶具有主动联系的优点。另一个优点是，从所提出的用于分析渐近稳定性的准则导出的相应渐近稳定性定理仅受到分数阶变化的轻微影响。此外，将统一稳定性判据应用于一般多维非线性时滞分数阶系统，将矢量Lyapunov函数与M矩阵方法相结合，应用相应的渐近稳定性判据。与传统稳定性判据相比，统一稳定性判据受分数阶变化和大时滞的影响较小。通过三个有代表性的算例验证了新型均匀稳定性判据的可靠性和有效性。