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arXiv · 2606.14401

A Feedback Stability Theorem for Frequency-dependent Compensation of Excess and Lack of Passivity

Pol Jane-Soneira·Gösta Stomberg·Ognjen Stanojev·Orcun Karaca·Lennart Harnefors
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Abstract

This article studies the stability of feedback interconnections of linear time-invariant systems based on frequency-dependent passivity indices. Using these frequency-dependent passivity indices, we show that the feedback interconnection of two systems can be certified to be stable even if both systems have a lack of passivity in terms of their scalar passivity indices. The main contribution of this paper is a new stability theorem based on frequency-dependent passivity indices. Moreover, we discuss the connection of the proposed feedback stability theorem to prior results based on scalar passivity indices. A numerical case study showcases the advantages of frequency-dependent passivity indices over scalar indices for feedback interconnections of linear systems.

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Pol Jane-Soneira, Gösta Stomberg, Ognjen Stanojev, Orcun Karaca, Lennart Harnefors. 2026-06-12. A Feedback Stability Theorem for Frequency-dependent Compensation of Excess and Lack of Passivity. https://arxiv.org/abs/2606.14401

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