New results are put forward for consensus analysis of high-order multi-agent network from the perspective of algebraic theory, subject to the application problem of existing consensus analysis achievements of first-order directed network in high-order network. Under certain condition, the system matrix of directed network is Metzler with zero row sum by model transformation where the dynamics of agents is modeled as a high-order integrator. Thus the analysis results of first-order consensus algorithms are extended to high-order ones using algebraic theory, nonnegative matrix theory and control theory. The consensus conditions and consensus states are proposed for leaderless and leader-follower cases in fixed topology. Moreover, it is proved that the whole closed-loop network achieves consensus asymptotically if the u-nion of directed graphs across finite switching intervals has a spanning tree in dynamic switching topology. Simulation examples and multi-vehicle formation control simulation validate the soundness of the theoretical results.%针对已有的一阶有向网络一致性分析结果在高阶网络的应用问题,从图论角度入手,给出了高阶多智能体网络一致性分析的新结果.通过模型变换,在一定条件下,将个体动态为高阶积分器模型的有向网络的系统矩阵变换为具有零行和的Metzler矩阵.由此采用图论、非负矩阵理论和控制理论工具,将一阶有向网络的一致性分析结果拓展到了高阶情况.针对固定拓扑,分别给出无领航和领航-跟随两种情况下的一致性条件及一致状态.并且证明动态拓扑情况下,在有限的拓扑切换时间间隔内,若有向图联合具有生成树,则整个闭环动态网络实现渐近一致.仿真实例和多车辆编队控制仿真验证了分析结果的正确性.
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