论文标题
非线性系统阶段
Phase of Nonlinear Systems
论文作者
论文摘要
在本文中，我们从输入输出的角度提出了一类称为半扇形系统的稳定非线性系统的相位定义。该定义涉及希尔伯特变换是使实现信号复杂的关键工具，因为相位最自然地在复杂域中出现。提出的非线性系统阶段，作为$ \ Mathcal {l} _2 $ gain的对应物，量化了被动性，并且与消散性高度相关。它还具有很好的物理解释，可以量化真实能量和反应能量之间的权衡。然后建立非线性小期定理，以进行半扇形系统的反馈稳定性分析。此外，通过使用乘数提出了广义版本。这些非线性小相定理概括了经典的消极定理的一个版本，并且最近出现的线性时间不变的小相定理。
In this paper, we propose a definition of phase for a class of stable nonlinear systems called semi-sectorial systems, from an input-output perspective. The definition involves the Hilbert transform as a critical instrument to complexify real-valued signals since the notion of phase arises most naturally in the complex domain. The proposed nonlinear system phase, serving as a counterpart of $\mathcal{L}_2$-gain, quantifies the passivity and is highly related to the dissipativity. It also possesses a nice physical interpretation which quantifies the tradeoff between the real energy and reactive energy. A nonlinear small phase theorem is then established for feedback stability analysis of semi-sectorial systems. Additionally, its generalized version is proposed via the use of multipliers. These nonlinear small phase theorems generalize a version of the classical passivity theorem and a recently appeared linear time-invariant small phase theorem.
