  In this paper, we extend the results from Jiao et al. (2019) on distributed
linear quadratic control for leaderless multi-agent systems to the case of
distributed linear quadratic tracking control for leader-follower multi-agent
systems. Given one autonomous leader and a number of homogeneous followers, we
introduce an associated global quadratic cost functional. We assume that the
leader shares its state information with at least one of the followers and the
communication between the followers is represented by a connected simple
undirected graph. Our objective is to design distributed control laws such that
the controlled network reaches tracking consensus and, moreover, the associated
cost is smaller than a given tolerance for all initial states bounded in norm
by a given radius. We establish a centralized design method for computing such
suboptimal control laws, involving the solution of a single Riccati inequality
of dimension equal to the dimension of the local agent dynamics, and the
smallest and the largest eigenvalue of a given positive definite matrix
involving the underlying graph. The proposed design method is illustrated by a
simulation example.
