We consider the problem of synchronizing a multi-agent system (MAS) composed of several identical linear systems connected through a directed graph.To design a suitable controller, we construct conditions based on Bilinear Matrix Inequalities (BMIs) that ensure state synchronization.Since these conditions are non-convex, we propose an iterative algorithm based on a suitable relaxation that allows us to formulate Linear Matrix Inequality (LMI) conditions.As a result, the algorithm yields a common static state-feedback matrix for the controller that satisfies general linear performance constraints.Our results are achieved under the mild assumption that the graph is time-invariant and connected.

翻译：我们考虑由多个通过有向图连接的相同线性系统组成的多智能体系统（MAS）的同步问题。为设计合适的控制器，我们构建了基于双线性矩阵不等式（BMI）的条件来确保状态同步。由于这些条件是非凸的，我们提出了一种基于合适松弛的迭代算法，从而能够构建线性矩阵不等式（LMI）条件。最终，该算法为控制器生成了一个满足一般线性性能约束的公共静态状态反馈矩阵。我们的结果在图是时不变且连通的温和假设下成立。