Analysis and design of output consensus algorithms for agents with linear dynamics

This paper deals with the consensus problem of linear systems from an integral perspective considering the dynamics of the agents and graph theoretical descriptions of the network. A consensus algorithm is defined as the interaction of two properties inherent to a network: hierarchical organization and information exchange. From this definition the problem is tackled as the stability of some coordination variables by means of Lyapunov functions and LMI methodology. This approach allows to define precision and speed indicators to evaluate the performance of different algorithms related to the agents´ dynamics. The main characteristics of this approach are discussed with the help of the consensus canonical example of double integrator systems and complemented with an analysis and design example.