Local pinning of networks of multi-agent systems with transmission and pinning delays

We study the stability of networks of multi-agent systems with local pinning strategies and two types of time delays, namely the transmission delay in the network and the pinning delay of the controllers. Sufficient conditions for stability are derived under specific scenarios by computing or estimating the dominant eigenvalue of the characteristic equation. In addition, controlling the network by pinning a single node is studied. Moreover, perturbation methods are employed to derive conditions in the limit of small and large pinning strengths.Numerical algorithms are proposed to verify stability, and simulation examples are presented to confirm the efficiency of analytic results.