On the necessity and sufficiency of discrete-time O'Shea-Zames-Falb multipliers
On the necessity and sufficiency of discrete-time O'Shea-Zames-Falb multipliers
复制标题
论离散时间 OShea-Zames-Falb 乘子的必要性和充分性
DOI：
10.1016/j.automatica.2023.110872
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发表时间：
2023
期刊：
影响因子：
6.4
通讯作者：
Su L
中科院分区：
文献类型：
--
作者：
Su L
研究由线性系统和有界单调非线性系统之间的反馈连接组成的离散Lurye系统的鲁棒稳定性。本文推测了一个合适的线性定常O’shea - zames - falb乘子的存在不仅是充分的，而且是必要的。粗略地说,一个成功的证据推测需要:(a)的乘数的二次曲线参数化描述的非线性,(b)的无损S-procedure展示不存在乘数意味着Lurye系统不均匀强劲稳定的非线性,以及(c)的存在乘数因子的设置中使用(a)意味着LTI乘法器的存在。我们研究了这三个步骤，展示了证明这一猜想的当前瓶颈。此外，我们提供了可用于反驳猜想的乘数类的扩展。
This paper considers the robust stability of a discrete-time Lurye system consisting of the feedback interconnection between a linear system and a bounded and monotone nonlinearity. It has been conjectured that the existence of a suitable linear time-invariant (LTI) O’Shea–Zames–Falb multiplier is not only sufficient but also necessary. Roughly speaking, a successful proof of the conjecture would require: (a) a conic parameterisation of a set of multipliers that describes exactly the set of nonlinearities, (b) a lossless S-procedure to show that the non-existence of a multiplier implies that the Lurye system is not uniformly robustly stable over the set of nonlinearities, and (c) the existence of a multiplier in the set of multipliers used in (a) implies the existence of an LTI multiplier. We investigate these three steps, showing the current bottlenecks for proving this conjecture. In addition, we provide an extension of the class of multipliers which may be used to disprove the conjecture.