  This paper is concerned with the distributed linear quadratic optimal control
problem. In particular, we consider a suboptimal version of the distributed
optimal control problem for undirected multi-agent networks. Given a
multi-agent system with identical agent dynamics and an associated global
quadratic cost functional, our objective is to design suboptimal distributed
control laws that guarantee the controlled network to reach consensus and the
associated cost to be smaller than an a priori given upper bound. We first
analyze the suboptimality for a given linear system and then apply the results
to linear multiagent systems. Two design methods are then provided to compute
such suboptimal distributed controllers, involving the solution of a single
Riccati inequality of dimension equal to the dimension of the agent dynamics,
and the smallest nonzero and the largest eigenvalue of the graph Laplacian.
Furthermore, we relax the requirement of exact knowledge of the smallest
nonzero and largest eigenvalue of the graph Laplacian by using only lower and
upper bounds on these eigenvalues. Finally, a simulation example is provided to
illustrate our design method.
