Recently, there have been a few developments reported on using the Wirtinger/free-matrix-based single integral inequality to stability problem of singular time-delay systems but there has been no report on the double ones. This paper presents an extension on applying the auxiliary function-based double integral inequality to the problem. Furthermore, an extension of the delay-dependent matrix technique into the single integral term of the Lyapunov–Krasovskii function to reduce more the conservatism has also been presented. By proposing an extended Lyapunov–Krasovskii functional (LKF) with triple integral terms and three delay-dependent matrices, a new delay-derivative-dependent stability criterion is derived. The effectiveness of the obtained result is illustrated through a numerical example.

最近，有一些关于使用基于 Wirtinger/自由矩阵的单积分不等式来解决奇异时滞系统稳定性问题的进展，但没有关于双不等式的报道。本文介绍了有关应用配件的功能扩展双积分不等式的问题。此外，还提出了延迟相关矩阵技术到 Lyapunov-Krasovskii 函数的单个积分项的扩展，以减少更多的保守性。通过提出具有三重积分项和三个时滞相关矩阵的扩展 Lyapunov-Krasovskii 泛函 (LKF)，推导出新的时滞导数相关稳定性准则。通过数值例子说明了所得结果的有效性。