An LQR-based Control design and gain tuning strategies proposals for a multi-agent system are presented in this article, the agents are connected in an undirected graph. Controller gains tuning are adjusted by selecting the Q and R weighting matrices of the Linear Quadratic Regulator. Agreement (consensus) is one of the fundamental problems in multi-agent control, where a set of agents must agree on a joint state value. In the proposed design, first considering that the behavior of the

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... protocol is undirected and static, the main objective is to highlight the complexity of the relationship between the convergence properties of this protocol and the structure of adjacent interconnections. The effects on the formation due to static geometry are analyzed from the resulting data according to the proximity between the agents, where behavior and stability are analyzed based on the desired formation geometry through the construction of the Laplacian matrix.