Matrix-Scaled Consensus on Switching Networks

This paper examines matrix-scaled consensus problems on switching networks where each agent holds time-varying matrix-valued scaling matrices that are either positive definite or negative definite. Matrix-scaled consensus amongst all agents can be achieved if the switching networks have frequent spanning trees and the scaling matrices remain unchanged within a time interval with a spanning tree. On time-varying networks, agents with the same time-varying scaling matrix will converge to the same point, differing from the virtual consensus value by the inverse of the scaling matrix. Both discrete-time and continuous-time cases are discussed. Simulation results are provided to demonstrate the theory.