Contents I. Introduction
In a multi-agent system, a fundamental task is to achieve consensus on a common state by all agents that interact by sharing their states (or information). One of the key requirements for such a task is to design consensus algorithms that are distributed, based only on local information available to the individual agent, under weak assumptions on the agents’ interconnection described by a graph. From this viewpoint, a myriad of important results have been developed for various agents’ models under different assumptions on the interconnection graph. First-order integrators have received an early attention which has led to identify significant problems in multi-agent networks such as average consensus, distributed optimization, and cooperative identification [1]–[5]. Inspired by these results, numerous solutions to the consensus problem of linear multi-agent systems governed by more complex dynamics, including second-order systems, linear oscillators, high-order multiple-integrators, and general linear dynamics, have been proposed in the literature under different assumptions on the interconnection graph topology (see, for instance, [6]– [15], to name only a few). Also, considerable efforts have been devoted to consensus problems in practical settings involving, for instance, communication delays [16]–[21] . The design of distributed consensus algorithms is more challenging on general directed graphs as compared with other algorithms benefiting from the induced symmetry of undirected networks. As a matter of fact, the nonsymmetry of directed graphs introduces multiple technical difficulties that are generally overcome to a price of additional assumptions on the availability of global information and, sometimes, on the information shared among agents.
