Abstract In this paper, we propose a new General Stability Criterion (GSC) for the stability analysis of the nonlinear fractional-order systems(FOs) with time delay at all levels based on the deduction of Wirtinger inequality, Integral mean value theorem(IMVT), fractional-order Lyapunov method, and our initiated general Lemma (WILL Deduction Method). This proposed WILL-Deduction method initiates a general lemma to simplify the construction of the GSC. Therefore, the GSC prevails over the previous criteria in that it solves the stability puzzle of all FOs, including all kinds of time-delay with greater flexibility. For all the fractional-order parameters α ∈ 0 , 1 , the GSC is effective. In conclusion, the initially proposed GSC has generality and universality with more efficiency. Finally the numerical simulations have proved the correctness and universality of GSC .

中文翻译：

---

基于WILL演绎法的时滞分数阶非线性系统新的一般稳定性判据

摘要 在本文中，我们基于 Wirtinger 不等式和积分平均值定理 (IMVT) 的推导，提出了一种新的通用稳定性判据 (GSC)，用于对各级具有时滞的非线性分数阶系统 (FO) 进行稳定性分析。 ，分数阶李雅普诺夫方法，以及我们发起的一般引理（WILL 演绎法）。这种提议的 WILL-Deduction 方法启动了一个通用引理来简化 GSC 的构造。因此，GSC 优于之前的标准，因为它以更大的灵活性解决了所有 FO 的稳定性难题，包括各种时延。对于所有分数阶参数 α ∈ 0 , 1 ，GSC 是有效的。综上所述，最初提出的GSC具有通用性和通用性，效率更高。