  This note investigates how to design topology structures to ensure the
controllability of multi-agent networks (MASs) under any selection of leaders.
We put forward a concept of perfect controllability, which means that a
multi-agent system is controllable with no matter how the leaders are chosen.
In this situation, both the number and the locations of leader agents are
arbitrary. A necessary and sufficient condition is derived for the perfect
controllability. Moreover, a step-by-step design procedure is proposed by which
topologies are constructed and are proved to be perfectly controllable. The
principle of the proposed design method is interpreted by schematic diagrams
along with the corresponding topology structures from simple to complex. We
show that the results are valid for any number and any location of leaders.
Both the construction process and the corresponding topology structures are
clearly outlined.
