  This work studies the problem of distributed optimization in heterogeneous
linear multi-agent systems. Instead of relying on a perfect communication
network as in many existing distributed optimization approaches, we considered
two important issues related to communication networks. First, assumed that
communication delays exist when each agent receives information from its
neighbors. Further, since communications networks are generally unreliable, we
assumed each agent interacted with the other agents through random digraphs.
Finally, to prove convergence to optimal solutions, delay-dependent sufficient
conditions are derived in the form of linear matrix inequality. An analysis of
numerical simulation results is presented to demonstrate the effectiveness of
the introduced approach.
