Group consensus protocol with input delay for HMASs in cooperative-competitive networks

This paper primarily examines group consensus (GC) in heterogeneous multi-agent systems (HMASs) within the context of cooperative-competitive networks and input delay. The agent dynamics are modeled using single and double integrators, while the complex network encompassing these agents demonstrate both cooperative and competitive relationships. We first propose control protocols incorporating delays to address GC in HMASs. Secondly, we establish algebraic criteria employing frequency-domain analysis techniques to ensure the achievement of GC in directed network topologies for HMASs, which is equally applicable to undirected networks. Following this, we conduct an extensive discussion to determine the upper boundary for permissible input delays in HMASs. Finally, simulations are performed to validate our theoretical findings and the algorithms.