Popov-Type Criterion for Consensus in Nonlinearly Coupled Networks

This paper addresses consensus problems in nonlinearly coupled networks of dynamic agents described by a common and arbitrary linear model. Interagent interaction rules are uncertain but satisfy the standard sector condition with known sector bounds; both the agent´s model and interaction topology are time-invariant. A novel frequency-domain criterion for consensus is offered that is similar to and extends the classical Popov´s absolute stability criterion.