This paper investigates the observability of discrete-time heterogeneous multi-agent systems (MASs) under an absolute protocol with switching topology and fixed topology, respectively, in which the agents are first-order and second-order integrator agents. By properly decomposing the adjacency matrix of such system into sub-matrices and selecting an appropriate output vector measured by the leaders, the dynamics of the heterogeneous MASs can be modelled as a classical LTI system. Based on switched theory, some algebraic features on the observability of discrete-time heterogeneous MASs are obtained by taking advantage of the invariant subspace for switching topology. Specially, an unobservable subspace is established by designing a switching sequence. Moreover, some necessary and/ or sufficient conditions for the observability of heterogeneous MASs with fixed topology are also derived by using Popov-Belevitch-Hautus (PBH) and the observable rank criteria based on the partitioned sub-matrices. Finally, numerical examples and simulations are given to show the theoretical results.

中文翻译：

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异构多智能体系统的可观察性

本文分别研究了具有切换拓扑和固定拓扑的绝对协议下离散时间异构多代理系统 (MAS) 的可观察性，其中代理是一阶和二阶集成代理。通过将此类系统的邻接矩阵适当地分解为子矩阵并选择由领导者测量的适当输出向量，异构 MAS 的动力学可以建模为经典的 LTI 系统。基于切换理论，利用切换拓扑的不变子空间，获得了离散时间异构MAS可观测性的一些代数特征。特别地，通过设计一个切换序列来建立一个不可观察的子空间。而且，通过使用 Popov-Belevitch-Hautus (PBH) 和基于分区子矩阵的可观察等级标准，还推导出了具有固定拓扑的异构 MAS 的可观察性的一些必要和/或充分条件。最后，给出了数值例子和仿真来说明理论结果。