Decentralized Frequency-Domain Conditions for D-Stability with Application to DC Microgrids
For networked control systems like DC microgrids, this method addresses confidentiality and communication barriers by providing a fully decentralized stability certification approach.
This paper proposes a decentralized frequency-domain method for regional pole placement (D-stability) in linearized networked systems, eliminating the need for shared subsystem models or communication. The method is applied to DC microgrids, enabling decentralized parameter synthesis via a broadcastable grid code, with numerical examples verifying its efficacy.
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.