离散时间Zames-Falb乘子的对偶界
Duality bounds for discrete-time Zames-Falb multipliers
AI总结：
本文基于Banach空间分离定理为离散时间Zames-Falb乘子建立相位限制，通过闭式或线性规划高效计算，并证明存在合适乘子的被控对象集合非凸。
摘要：
我们基于Banach空间的分离定理，为离散时间Zames-Falb乘子建立了相位限制。与连续时间情形相比，这些限制导致数值高效的结果，可以通过闭式形式或线性规划计算。闭式相位限制在构造满足等式的乘子意义下是紧的。我们讨论了数值例子，其中这些限制比文献中的其他限制更强。数值结果补充了文献中对乘子的搜索；它们使我们能够通过构造证明，存在合适Zames-Falb乘子的被控对象集合是非凸的。
英文摘要：
We develop phase limitations for the discrete-time Zames-Falb multipliers based on the separation theorem for Banach spaces. By contrast with their continuous-time counterparts they lead to numerically efficient results that can be computed either in closed form or via a linear program. The closed-form phase limitations are tight in the sense that we can construct multipliers that meet them with equality. We discuss numerical examples where the limitations are stronger than others in the literature. The numerical results complement searches for multipliers in the literature; they allow us to show, by construction, that the set of plants for which a suitable Zames-Falb multiplier exists is non-convex.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
