Bipartite containment control for discrete-time second-order multiagent systems with time-varying delays on switching signed topologies

Abstract

Compared with the traditional cooperative networks, the signed networks containing both cooperative and competitive interactions have prevailed. In light of such consideration, the problem of bipartite containment control for second-order multiagent systems (MASs) including multiple leaders over signed networks is investigated in this paper, in which time-varying delays and switching topologies are considered. Firstly, an augmented system method is explored such that the bipartite containment problem is formulated as the convergence problem of the product of an infinite number of sub-stochastic matrices. Then, by constructing a new leader–follower topology for each switching topology, the corresponding relationships between two topologies are used to simplify our model. Moreover, based on the properties of non-negative matrix and the technique of edge composition, a mild topological condition is developed for guaranteeing the bipartite containment collective behavior. Finally, numerical examples are presented for verifying the correctness of our conclusion.