This article exploits positive systems theory in the search for Zames–Falb multipliers for the analysis of discrete‐time Lurie systems, where the nonlinearity is assumed to be slope‐restricted. Although a similar problem has been tackled in a continuous time context, the results in discrete‐time take a different form and require a somewhat different approach to overcome certain technical problems. The work has two compelling features: (i) the arising algorithms are completely convex; and (ii) numerical results compare well with the state‐of‐the‐art in some cases, providing the least conservative result in one instance.

中文翻译：

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具有斜率受限非线性的离散系统：使用外部正性的Zames–Falb乘数分析

本文利用正系统理论来寻找Zames–Falb乘数以分析离散时间Lurie系统，在该系统中非线性被假定为斜率受限的。尽管在连续的时间范围内已经解决了类似的问题，但是离散时间的结果采用了不同的形式，并且需要略微不同的方法来克服某些技术问题。这项工作具有两个引人注目的特征：（i）产生的算法是完全凸的；（ii）在某些情况下，数值结果与最新技术水平相当，在一种情况下提供的保守性最低。