基于RISE控制方法的支持引理
Supporting Lemmas for RISE-based Control Methods
AI总结：
本文提出两个支持引理，用于证明RISE控制方法中误差符号积分性质的稳定性分析。
摘要：
一类称为鲁棒误差符号积分（RISE）的连续控制器在过去十年中被提出，用以实现非线性系统在受到外源干扰和/或模型不确定性下的跟踪误差渐近收敛。该类控制器的发展依赖于误差信号符号积分的性质。此前文献中未提供该性质的证明。通过微分包含分析某些RISE控制器的稳定性，此类结果依赖于一组点集是勒贝格可忽略的假设。本文陈述并证明了两个与该性质相关的引理。
英文摘要：
A class of continuous controllers termed Robust Integral of the Signum of the Error (RISE) have been published over the last decade as a means to yield asymptotic convergence of the tracking error for classes of nonlinear systems that are subject to exogenous disturbances and/or modeling uncertainties. The development of this class of controllers relies on a property related to the integral of the signum of an error signal. A proof for this property is not available in previous literature. The stability of some RISE controllers is analyzed using differential inclusions. Such results rely on the hypothesis that a set of points is Lebesgue negligible. This paper states and proves two lemmas related to the properties.
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