What is the critical condition for a Laplacian Matrix representing the inter-agent communication graph of a networked dynamical system with delay in the information exchange between agents?
The critical condition for a Laplacian Matrix representing the inter-agent communication graph of a networked dynamical system with delay is that all the non-zero eigenvalues of the Laplacian matrix have positive real parts. This ensures the system's stability despite the delays in information exchange between agents.