LeaderBased Consensus in Directed Networks of Homogeneous Positive Agents With Multiple Inputs

Abstract

In this paper, the nonzero finite positive state consensus problem of leaderfollowing multiagent systems (MASs) connected over a directed network is investigated. The multiagent network consists of homogeneous linear timeinvariant (LTI) positive agents whose minimal positive statespace realization is assumed to be known. In this paper, a statefeedback hierarchical control protocol is proposed where the local controller synthesizes a singular, Lyapunov stable, and Metzler system matrix with a simple dominant eigenvalue at origin. The obtained consensus vector is the positive eigenvector associated with the zero eigenvalue of the synthesized system matrix. The controller gain matrices are obtained by solving a set of necessary and sufficient conditions derived in linear programing framework. A numerical example is given to elucidate the usefulness of the proposed results.