Output Synchronisation in Heterogeneous Networks with Nonlinear Couplings

This paper investigates the output synchronisation problem in heterogeneous networks with nonlinear couplings. We present conditions that connect network heterogeneity with the graph structure, establishing criteria for synchronisation in two distinct settings. First, we consider networks where each agent’s dynamics approximate a nominal reference model, deriving conditions that ensure synchronisation for agents with bounded deviations from this model. In the second setting, without a nominal reference, we focus on properties between adjacent agents and propose a synchronisation condition that relies only on these local properties, allowing for greater heterogeneity among non-adjacent agents. For both settings, sector-bounded nonlinear couplings are considered. Together, these results provide a flexible framework for achieving synchronisation in networks with varying degrees of heterogeneity, illustrated through examples.