Exact computation of maximal allowable delay for general second-order multi-agents consensus

The delay consensus margin (DCM) defines the largest delay range within which a distributed feedback control protocol can achieve and maintain the consensus robustly against uncertain time delays. This article investigates the exact computation of the DCM for general second-order multi-agent systems (MASs) under distributed proportional-derivative (PD) feedback, or alternatively known as position and velocity feedback protocols over undirected graphs. We consider MASs with uncertain constant delays, and derive the DCM expression for second-order agents and show that it can be determined by solving a non-smooth quasi-concave optimization problem. The DCM as such, can be computed via convex optimization methods.