In this paper, the problem of delay-dependent stability analysis of fractional-order systems with time-varying delay is investigated. First, a class of novel fractional-order integral inequalities for quadratic functions by constructing appropriate auxiliary functions is proposed, which has been proven to be useful in analyzing fractional-order systems with time-varying delay. Based on these proposed inequalities, the Lyapunov–Krasovskii functions are designed to deal with the time-varying delay terms, reducing the conservatism of the stability criteria. Furthermore, delay-dependent criteria are derived to achieve asymptotic stability of fractional-order systems with time-varying delay. Finally, two examples are provided to illustrate the effectiveness and feasibility of the proposed stability criteria.

研究具有时变时滞的分数阶系统的时滞相关稳定性分析问题。首先，通过构造适当的辅助函数，提出了一类新颖的二次函数分数阶积分不等式，已被证明对于分析时变时滞分数阶系统是有用的。基于这些提议的不等式，设计了Lyapunov–Krasovskii函数来处理时变时滞项，从而降低了稳定性标准的保守性。此外，推导依赖于时延的准则，以实现具有时变时滞的分数阶系统的渐近稳定性。最后，提供了两个示例来说明所提出的稳定性标准的有效性和可行性。