Energy-Aware Consensus Algorithms in Networked Sampled Systems

This work presents a method to analyze the convergence to consensus of a network of first order linear systems, when the signals associated to the interconnections are sampled from the continuous time systems. In order to minimize the energy consumed in the process of communication, we will look for the optimal sampling time such that the consensus is reached in a minimum number of iterations (communications). The analysis is performed by minimizing several objective functions that take into account a measure of the convergence rate to reach a consensus. These objective functions mainly depend on the eigenvalues of the sampled transition matrix of the system. Finally, we present a case study based on the torus topology, where a simple case of communication is analyzed and the optimal sampling time to reach a consensus is obtained.