Observability of Heterogeneous Multi-Agent Systems

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.