Deviation bounds in multi agent systems described by undirected graphs

The theory of port-Hamiltonian systems is used to derive upper bounds for the state deviations in multi-agent systems described by undirected graphs pinned to a reference signal. The upper bounds for the deviations in networks of first or second order agents, respectively, depend on the minimal eigenvalue of the extended Laplacian of the system. In networks of first order agents, the deviations decay exponentially with a rate depending on the same minimal eigenvalue. In case networks of second order systems meet specific design properties, it can be shown that the deviations also decay exponentially with half the rate compared to first order systems.