中文摘要：

我们与将军一起考虑一套多代理人系统(质量) 线性时间不变(LTI ) 动力学和性能索引联合系统的行为的一个控制问题。在代理人之间的互联拓扑学与自我环作为一台未受指导的小型旋转式印刷机被建模，在每个系统是一个节点，在每个节点的控制行动是它的状态的功能和它的邻居的状态的地方。在这份报纸考虑的线性二次的管理者(LQR ) 控制问题能在反馈获得上由于块对角线限制被认为是一个结构优化问题。它被看那在最小化一个单个代理人系统的和性能的分布式的控制器平等者下面最小化多代理人系统的 LQR 性能限制。一个足够的条件以一套线性矩阵不平等(LMI ) 被介绍完成某些非最优的表演说明。除了使控制设计更适用， LQR 表演区域的观点被介绍并且分析，它被显示关于拉普拉斯算符矩阵的特征值凸。多代理人系统的 LQR 控制然后被变换成一套分系统的 LQR 控制，它作为系数与最小、最大的特征值合并二仅仅不平等限制。数字例子被举说明建议方法。

英文摘要：

We consider a set of multi-agent systems （MASs） with general linear time-invariant （LTI） dynamics and a control problem where the performance index couples the behavior of the system. The interconnection topology between the agents is modeled as an undirected multi-graph with self-loop, where each system is a node and the control action at each node is a function of its state and the states of its neighbors. The linear quadratic regulator （LQR） control problem considered in this paper can be regarded as a structure optimization problem due to the block diagonal restriction on the feedback gain. It is shown that minimizing the LQR performance limit of the multiagent system under the distributed controller equals minimizing the sum performance of a single agent system. A sufficient condition is presented in terms of a set of linear matrix inequalities （LMIs） to achieve certain suboptimal performance specifications. In addition to make the control design more applicable, the notion of the LQR performance region is introduced and analyzed, which is shown to be convex with respect to the eigenvalues of the Laplacian matrix. The LQR control of the multi-agent system is then converted to the LQR control of a set of subsystems, which incorporates only two inequality constraints with the minimum and maximum eigenvalues as the coefficients. Numerical examples are presented to illustrate the proposed method.