标题： 一种线性耗散性方法用于一类正Lur'e系统的增量输入到状态稳定性 显示英文标题

标题： A linear dissipativity approach to incremental input-to-state stability for a class of positive Lur'e systems

摘要： 对于具有特定正性结构的受迫非线性微分方程系统，考虑了增量稳定性性质。 针对所考虑的Lur'e系统的输入/状态/输出轨迹对，推导出一个增量稳定性估计，由此得到若干结论，包括增量指数输入-状态稳定性性质以及某些具有线性增益的输入输出稳定性概念。 增量稳定性估计为研究收敛和（几乎）周期性强迫项的响应提供了基础，并且目前对此进行了探讨。 我们的结果表明，当对非线性项施加增量增益条件时，正Lur'e系统的实Aizerman猜想的增量版本是正确的，如我们所述。 我们的论证得到了线性耗散性理论的支持——这是正线性控制系统的属性。 显示英文摘要

摘要： Incremental stability properties are considered for certain systems of forced, nonlinear differential equations with a particular positivity structure. An incremental stability estimate is derived for pairs of input/state/output trajectories of the Lur'e systems under consideration, from which a number of consequences are obtained, including the incremental exponential input-to-state stability property and certain input-output stability concepts with linear gain. Incremental stability estimates provide a basis for an investigation into the response to convergent and (almost) periodic forcing terms, and is treated presently. Our results show that an incremental version of the real Aizerman conjecture is true for positive Lur'e systems when an incremental gain condition is imposed on the nonlinear term, as we describe. Our argumentation is underpinned by linear dissipativity theory -- a property of positive linear control systems.