Pinning Synchronization of Heterogeneous Multi-Agent Nonlinear Systems via Contraction Analysis

Using recent results on the incremental stability analysis via contraction and on internal model principle, we revisit the pinning synchronization problem in nonlinear multi-agent systems (MAS). We provide sufficient and necessary conditions for both the pinned agents as well as the rest of the agents to guarantee the state synchronization. For the non-pinned agents, we present a distributed control framework based only on the relative local state measurement and we give sufficient conditions for the contractivity of the individual virtual systems in order to achieve pinning synchronization. Numerical simulation is given to illustrate the main results.