  In this paper, the time-varying formation and time-varying formation tracking
problems are solved for linear multi-agent systems over digraphs without the
knowledge of the eigenvalues of the Laplacian matrix associated to the digraph.
The solution to these problems relies on a framework that generalizes the
directed spanning tree adaptive method, which was originally limited to
consensus problems. Necessary and sufficient conditions for the existence of
solutions to the formation problems are derived. Asymptotic convergence of the
formation errors is proved via graph theory and Lyapunov analysis.
