  This paper presents a unified framework of time-varying formation (TVF)
design for general linear multi-agent systems (MAS) based on an observer
viewpoint from undirected to directed topology, from stabilization to tracking
and from a leader without input to a one with bounded input. The followers can
form a TVF shape which is specified by piecewise continuously differential
vectors. The leader's trajectory, which is available to only a subset of
followers, is also time-varying. For the undirected formation tracking and
directed formation stabilization cases, only the relative output measurements
of neighbors are required to design control protocols; for the directed
formation tracking case, the agents need to be introspective (i.e. agents have
partial knowledge of their own states) and the output measurements are
required. Furthermore, considering the real applications, the leader with
bounded input case is studied. One main contribution of this paper is that
fully distributed adaptive output protocols, which require no global
information of communication topology and do not need the absolute or relative
state information, are proposed to solve the TVF control problem. Numerical
simulations including an application to nonholonomic mobile vehicles are
provided to verify the theoretical results.
