Zames-Falb多倍体的相限制
Phase limitations of Zames-Falb multipliers
AI总结：
本文分析了连续时间和离散时间Zames-Falb多倍体的相限制及其与Kalman猜想的关系，提出了一种连续时间多倍体的相限制扩展，并展示了离散时间多倍体的新相限制及其在Kalman猜想反例中的应用。
摘要：
连续时间和离散时间Zames-Falb多倍体及其与Kalman猜想的关系得到了分析。Megretski提出的连续时间多倍体的相限制被推广并澄清了其适用性；通过文献中的经典例子展示了其与Kalman猜想的关系。证明了存在第四阶系统，其中合适的Zames-Falb多倍体不存在且模拟显示不稳定行为。开发了一种新的离散时间Zames-Falb多倍体相限制。其应用通过第二阶Kalman猜想反例进行演示。最后，利用离散时间限制证明在离散时间域中不可能存在Kalman猜想的直接对应物。
英文摘要：
Phase limitations of both continuous-time and discrete-time Zames-Falb multipliers and their relation with the Kalman conjecture are analysed. A phase limitation for continuous-time multipliers given by Megretski is generalised and its applicability is clarified; its relation to the Kalman conjecture is illustrated with a classical example from the literature. It is demonstrated that there exist fourth-order plants where the existence of a suitable Zames-Falb multiplier can be discarded and for which simulations show unstable behavior. A novel phase-limitation for discrete-time Zames-Falb multipliers is developed. Its application is demonstrated with a second-order counterexample to the Kalman conjecture. Finally, the discrete-time limitation is used to show that there can be no direct counterpart of the off-axis circle criterion in the discrete-time domain.
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