基于自由权矩阵的时变时延线性群系统编队控制

研究了基于自由权矩阵方法的时变时延线性群系统编队控制问题。首先，基于一致性理论，设计了具有时变时延的线性群系统编队控制协议。其次，通过变量代换，将时延条件下的线性群系统编队控制问题转化为时延系统的镇定问题。构造Lyapunov-Krasovskii函数，并利用自由权矩阵方法对时延系统的镇定问题进行分析，得到了保守性较小的线性矩阵不等式（LMI）判据，并求解出时延上界和编队控制器增益。最后，通过仿真实验，验证了方法的有效性。

Formation control for linear swarm systems with time-varying delays based on free-weighting matrices

Based on free-weighting matrices method, the formation control for the linear swarm systems with time-varying delays is investigated. First, a protocol for the formation control with time-varying delays is proposed based on consensus theory. Second, the formation control problem is transformed into the stabilization problem of delay-dependent system using variable substitution. The Lyapunov-Krasovskii function is constructed, and the stabilization problem of the delay-dependent system is analyzed using free-weighting matrices method. Then, the Linear Matrix Inequality (LMI) criterion with lower conservatism is obtained. The upper bounds of delays and the controller gains are also given. Finally, the effectiveness of the method is verified through the simulation experiments.