  In this study, we propose a design methodology of distributed controllers for
multi-agent systems on a class of directed interaction networks by extending
the gradient-flow method. Although the gradient-flow method is a common design
tool for distributed controllers, it is inapplicable to directed networks.
First, we demonstrate how to construct a distributed controller for systems
over a class of time-invariant directed graphs. Subsequently, we establish
better convergence properties and performance enhancement than the conventional
gradient-flow method. To illustrate its application in time-varying networks,
we address the dynamic matching problem of two distinct groups of agents with
different sensing ranges. This problem is a novel coordination task that
involves pairing agents from two distinct groups to achieve a convergence of
the paired agents' states to the same value. Accordingly, we apply the proposed
method to this problem and provide sufficient conditions for successful
matching. Lastly, numerical examples for systems on both time-invariant and
time-varying networks demonstrate the effectiveness of the proposed method.
