The Singular Angle of Nonlinear Systems

Chao Chen; Di Zhao; Sei Zhen Khong

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arXiv · 2109.01629

The Singular Angle of Nonlinear Systems

Chao Chen·Di Zhao·Sei Zhen Khong

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Abstract

In this paper, we introduce an angle notion called the singular angle for nonlinear systems from an input-output perspective. The proposed system singular angle, based on the angle between $L_2$-signals, describes an upper bound for the ''rotating effect'' from system input to output signals. It quantifies passivity and serves as a counterpart to system $L_2$-gain. It also provides an alternative to a recently defined notion of system phase which adopts complexification of real-valued signals via the Hilbert transform. A nonlinear small angle theorem is established for feedback stability analysis, which involves a comparison of the loop system angle with $\pi$. The theorem generalizes the classical passivity theorem via a tradeoff between the singular angles of open-loop systems.

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Chao Chen, Di Zhao, Sei Zhen Khong. 2021-09-03. The Singular Angle of Nonlinear Systems. https://arxiv.org/abs/2109.01629

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