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arXiv · 2605.13529

Decentralized Frequency-Domain Conditions for D-Stability with Application to DC Microgrids

Zelin Sun·Shanshan Jiang·Xiaoyu Peng·Xiang Zhu·Xiuqiang He·Hua Geng
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Abstract

This paper proposes a decentralized method for regional pole placement, or $\mathcal{D}$-stability, in linearized networked systems. Existing LMI-based methods are hindered by confidentiality concerns regarding proprietary subsystem models and the absence of communication infrastructures. To overcome these barriers, we map the target region $\mathcal{D}$ of pole placement to an auxiliary left-half plane and introduce positive functions to handle the resulting complex-coefficient dynamics. We prove that $\mathcal{D}$-stability is guaranteed via local frequency-domain criteria without requiring shared subsystem models or inter-subsystem communication. This method is then tailored to DC microgrids, where a loop transformation is utilized to reallocate the burden of stability certification, deriving a broadcastable grid code for decentralized parameter synthesis. Numerical examples verify the efficacy of the proposed method.

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Zelin Sun, Shanshan Jiang, Xiaoyu Peng, Xiang Zhu, Xiuqiang He, Hua Geng. 2026-05-13. Decentralized Frequency-Domain Conditions for D-Stability with Application to DC Microgrids. https://arxiv.org/abs/2605.13529

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