Abstract In this paper, the problem of simultaneously reconstructing the states and delays for nonlinear systems subject to input delays is studied. To relax some limitations of the classical Lipschitz condition, the one-sided Lipschitz and quadratically inner-bounded conditions are employed to handle nonlinearities. The control inputs are subject to bounded unknown time-varying delays. To deal with this open and interesting problem, we propose a sliding mode observer based method to simultaneously estimate the states and identify the unknown delays of the systems without making assumption on differentiability of the delays. Furthermore, our method does not require the minimum phase condition that is common in sliding mode observer based schemes. The effectiveness of the proposed method is illustrated by a numerical example.

中文翻译：

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具有输入延迟的非线性系统的状态和延迟重建

摘要 本文研究了受输入时滞影响的非线性系统的状态和时滞同时重构问题。为了放宽经典 Lipschitz 条件的一些限制，采用单边 Lipschitz 和二次内界条件来处理非线性。控制输入​​受到有界未知时变延迟的影响。为了解决这个开放而有趣的问题，我们提出了一种基于滑模观测器的方法来同时估计状态和识别系统的未知延迟，而无需对延迟的可微性进行假设。此外，我们的方法不需要在基于滑模观测器的方案中常见的最小相位条件。通过数值例子说明了所提出方法的有效性。