  This paper is concerned with robust instability analysis for linear
multi-agent dynamical systems with cyclic structure. This relates to
interesting and important periodic oscillation phenomena in biology and
neuronal science, since the nonlinear phenomena often occur when the linearized
model around an equilibrium point is unstable. We first make a problem setting
on the analysis and define the notion of robust instability radius (RIR) as a
quantitative measure for maximum allowable stable dynamic perturbation in terms
of the H-infinity norm. After showing lower bounds of the RIR, we derive the
exact RIR, which is analytic and scalable, for first order time-lag agents.
Finally, we make a remark on the potential applicability to some classes of
higher order systems.
