This paper provides a topology based analysis for the average consensus problem regarding various configurations and possibilities. Consensus problem which can be defined as the agreement of the agents in a multi-agent topology is a common problem in various fields of science, technology and engineering. The main subject focused on within the scope of this study, is the selection of the topology regarding various performance criteria for the agents to reach consensus. Basic concepts of multi-agent systems are introduced along with an algebraic background. Graph Theory and its properties are also covered as a basis for understanding the behavior of multi-agent systems. A numerical approach in order to determine the structure of the connection topology that satisfies the predefined performance criteria, is proposed. In the end, case studies are included to verify the effectiveness of the proposed method.
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