Multi-agent consensus over signed graphs with switching topology, L. Wang, A. Fontan, Y. Hong, G. Shi, and Claudio Altafini,
has been been accepted for publication in the 20th European Control Conference (ECC), London, UK, July 2022
Abstract: Laplacian dynamics on signed graphs have a richer behavior than those on nonnegative graphs. In particular, their stability is not guaranteed a priori. Consequently, also the time-varying case must be treated with care. In particular, instabilities can occur also when switching in a family of systems each of which corresponds to a stable signed Laplacian. In the paper we obtain sufficient conditions for such a family of signed Laplacians to form a consensus set, i.e., to be stable and converging to consensus for any possible switching pattern. The conditions are that all signed Laplacian matrices are eventually exponentially positive (a Perron Frobenius type of property) and normal.