Design of distributed observer-based controllers for bipartite containment of discrete-time descriptor MASs over signed digraphs

In this article, the bipartite containment control problem is considered for discrete-time linear descriptor multi-agent systems (DMASs) with multiple dynamic leaders under fixed signed digraph topology, in which each leader can be autonomous or evolving dynamically via communicating with other leaders in its neighbourhood. Based upon the properties of the solutions to discrete-time modified generalised algebraic Riccati equations(MGAREs), three different types of distributed observer-based protocols utilising only available local information are devised. Algorithms for constructing the devised protocols are also presented. Moreover, sufficient conditions ensuring the bipartite containment of the DMASs are established. Finally, the effectiveness of the presented protocols is validated by numerical simulations.