Generalized Nyquist Consensus Condition for Linear Multi Agent Systems with Heterogeneous Delays

We study robust consensus of linear Multi-Agent Systems (MAS) with heterogeneous delays. We provide a very accurate set-valued condition that guarantees consensus for arbitrary bounded delays and arbitrary connected topologies. This condition is proven using the generalized Nyquist criterion. From the set-valued condition, an explicit analytical formula is derived for single integrator MAS. In this publication, the delays affect both the agent's own state and its neighbor's state; and we assume that the delay of the agent's own state and its neighbor's state are different, e.g. due to a combination of computation delays, which affect both states, and transmission delays, which only affect the neighbor's state.