  We consider the problem of synchronizing a multi-agent system (MAS) composed
of several identical linear systems connected through a directed graph.To
design a suitable controller, we construct conditions based on Bilinear Matrix
Inequalities (BMIs) that ensure state synchronization.Since these conditions
are non-convex, we propose an iterative algorithm based on a suitable
relaxation that allows us to formulate Linear Matrix Inequality (LMI)
conditions.As a result, the algorithm yields a common static state-feedback
matrix for the controller that satisfies general linear performance
constraints.Our results are achieved under the mild assumption that the graph
is time-invariant and connected.
