On Semidefiniteness of Signed Laplacians with Application to Microgrids

Wei Chen, Dan Wang, Ji Liu, Tamer Başar, Karl H. Johansson, Li Qiu

Research output: Contribution to journalArticlepeer-review


The paper investigates the positive semidefiniteness of signed Laplacians. It is noted that a symmetric signed Laplacian defines a unique resistive electrical network, wherein the negative weights correspond to negative resistances. As such, the positive semidefiniteness of the signed Laplacians is equivalent to the passivity of the associated resistive networks. By utilizing n-port circuit theory, we obtain several equivalent conditions for signed Laplacians to be positive semidefinite with a simple zero eigenvalue. These conditions characterize a set of negative weights that maintain the semidefiniteness of the Laplacian. The results are used to analyze the small-disturbance angle stability of microgrids as an application.

Original languageEnglish (US)
Pages (from-to)97-102
Number of pages6
Issue number22
StatePublished - 2016

ASJC Scopus subject areas

  • Control and Systems Engineering


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