Matrix-Scaled Consensus Over Undirected Networks

This paper studies matrix-scaled consensus algorithms for linear dynamical agents interacting over an undirected network. Under the proposed algorithms, the state vectors of all agents asymptotically agree up to some scaling matrix weights. First, the geometry of the matrix-scaled consensus space and the matrix-scaled Laplacian are studied. Second, matrix-scaled consensus algorithms for networks of single-integrators are proposed in two scenarios: with and without constant parametric uncertainties. Nonlinear and finite-time matrix-scaled consensus algorithms are also discussed. Finally, observer-based matrix-scaled consensus algorithms are designed for homogeneous and then extended for heterogeneous linear-time invariant agents. The validity of the proposed algorithms is established through rigorous mathematical analysis and demonstrated by numerical simulations.