This paper presents the stability analysis problem of fractional-order nonlinear systems with time-varying delay. After formulating the problem and selecting the nonlinear model as the system under study, stability analysis and expression of the sufficient conditions for fractional-order nonlinear systems with time-varying delay are obtained using two different methods. In these methods, sufficient conditions for stability of fractional-order nonlinear systems are found in the form of satisfying some inequalities based on norms of nonlinear functions in the system and in terms of linear matrix inequality according fractional-order and nonlinear functions. In each case, despite the presence of time-varying delay, the system stability is ensured by meeting the stability sufficient conditions in terms of an inequality of functions and system parameters. Finally, numerical examples are given to determine the effectiveness of the proposed theorem.

提出了具有时变时滞的分数阶非线性系统的稳定性分析问题。在提出问题并选择非线性模型作为研究系统之后，使用两种不同的方法获得了具有时变时滞的分数阶非线性系统的稳定性分析和充分条件的表示。在这些方法中，基于满足系统非线性函数范数的不等式以及根据分数阶和非线性函数的线性矩阵不等式，找到了满足分数阶非线性系统稳定性的充分条件。在每种情况下，尽管存在时变延迟，通过在功能和系统参数的不等式方面满足稳定性的充分条件，可以确保系统的稳定性。最后，通过数值例子来确定所提出定理的有效性。