Observer-based leader-following cluster consensus for positive multi-agent systems with input time-varying delay

This work aims to analyse the cluster consensus for positive multi-agent systems (MASs) with nonlinearities. This study focuses on introducing an observer-based controller with the aim of achieving cluster consensus in the considered positive nonlinear MASs, where the controller includes time-varying delay. Specifically in cluster consensus, agents are divided into multiple clusters to accomplish various collective tasks, each influenced by distinct inter-cluster and intra-cluster communications. In this study, a fixed directed graph is employed to express the communication among agents. By designing a proper Lyapunov-Krasovskii functional and utilising the properties of graph, a set of conditions required for cluster consensus of the examined MASs is established as linear matrix inequalities. Finally, the effectiveness of the derived theoretical findings is confirmed through numerical examples.