Adaptive Event-Triggered Bipartite Containment Control of Linear Multiagent Systems Under Directed Topologies

This article focuses on the adaptive event-triggered bipartite containment problem of linear multiagent systems (MASs) under the signed digraphs, where multiple leaders with zero and nonzero inputs are respectively considered. Based on the relative states of neighbor agents, the fully distributed event-triggered control protocols are proposed to make containment error converge to zero. It is noted that the adaptive control is adopted to avoid the use of the global information, i.e., the number of agents in the MAS, the eigenvalues of Laplace matrix, etc. Since the signed digraph is considered, the Laplace matrix is asymmetric, which greatly increases the design difficulty of adaptive event-triggered strategy and is challenging. To solve this problem, innovative compound triggering conditions are designed, under which neighbors not only communicate intermittently, but also control protocols are updated discontinuously only at their own triggering instants. Finally, the theoretical results obtained in this article are verified by two examples.