The consensus problem in the behavioral approach

In this paper we present some preliminary results about the consensus problem in the behavioral approach. Specifically, we consider a group of N homogeneous agents whose dynamics are described by the same (linear and time-invariant) behavioral model, involving inputs, measurable variables and target variables. We assume that the agents' mutual communication is described by some (not necessarily symmetric) adjacency matrix. In this set-up we have derived necessary and sufficient conditions for a group of homogenous dynamic controllers, making use of the weighted information received by each agent about the other agents' dynamics, for the N agents to achieve consensus on the target variables dynamics (under regularity constraints on the overall interconnection). Such conditions have been extended to the case when consensus is searched for both the target and the measurable variables. Finally, it is shown that the paper results encompass, as a special case, the classical situation when the agents' dynamics are described by state-space models and the target (measurable) variables are the state (output) variables.