针对一般线性二阶多智能体系统, 设计仅含采样位移信息的分布式脉冲一致性控制算法。利用谱分析和拟周期齐次Lyapunov函数方法, 给出能够实现二阶一致性的判据, 揭示采样周期、控制器增益以及拉普拉斯矩阵的特征值对实现二阶一致性的影响机理。进一步分析采样周期和系统参数的不确定性对分布式脉冲一致性算法的影响, 并以低维数的线性矩阵不等式, 给出了能够实现鲁棒二阶一致性的充分条件。最后, 通过数值例子验证了所提出的理论结果。

As for general linear second-order multi-agent systems,a distributed impulse consensus control algorithm with sampled displacement information is designed.By using the methods of spectral analysis and quasi-periodic homogeneous Lyapunov function,the criteria for achieving second-order consensus are given, which reveal the mechanism of quantitative effects of the sampling period,the controller gain and the eigenvalue of Laplace matrix on achieving second-order consensus.The influence of the sampling period and uncertainties of system parameters on the distributed impulse consensus algorithm is further analyzed,and the sufficient conditions for achieving robust second-order consensus are given in the form of low-dimensional linear matrix inequalities.Finally,numerical examples have verified the proposed theoretical results.