This paper presents a method based on a continuity argument for analysing the delay robustness of nonlinear control systems with uncertainties. In particular, a delay-dependent stability condition is established in the form of a norm inequality for an adaptive control system with a time delay in the control input. The continuous dependence of the condition on the delay is derived via the uniform continuity in the delay of the fundamental solution of a general linear time-varying delay-differential equation. Since the stability condition holds when the delay is zero, the condition must be true for a certain non-zero positive delay due to continuity. Numerical simulations show the performance and robustness of the control system in the presence of an input delay. Remarkably, the results also illustrate a close agreement with the dependence on control parameters of the transient performance bounds predicted by the theoretical analysis in this paper.

中文翻译：

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拉格朗日系统的自适应控制器的一致连续性和时滞鲁棒性

本文提出了一种基于连续性参数的不确定性非线性控制系统的时滞鲁棒性分析方法。尤其是，对于在控制输入中具有时间延迟的自适应控制系统，以标准不等式的形式建立了与延迟有关的稳定性条件。通过一般线性时变时滞微分方程基本解的时延的一致连续性得出条件对时延的连续依赖性。由于当延迟为零时稳定性条件成立，因此由于连续性，对于某些非零正延迟，条件必须为真。数值模拟显示了存在输入延迟时控制系统的性能和鲁棒性。值得注意的是