  This paper provides a framework to characterize the gain margin, phase
margin, and maximum input delay margin of a linear time-invariant multi-agent
system where the interaction topology is described by a graph with a directed
spanning tree. The stability analysis of the multi-agent system based on the
generalized Nyquist theorem is converted to finding a minimum gain positive
definite Hermitian perturbation and minimum phase unitary perturbation in the
feedback path of the loop transfer function. Specifically, two constrained
minimization problems are solved to calculate the gain, phase, and input delay
margins of the multi-agent system. We further state necessary and sufficient
conditions concerning stability of the multi-agent system independent of gain
and phase perturbations, and input delay.
