  We consider a linear time-invariant system in discrete time where the state
and input signals satisfy a set of integral quadratic constraints (IQCs).
Analogous to the autonomous linear systems case, we define a new notion of
spectral radius that exactly characterizes stability of this system. In
particular, (i) when the spectral radius is less than one, we show that the
system is asymptotically stable for all trajectories that satisfy the IQCs, and
(ii) when the spectral radius is equal to one, we construct an unstable
trajectory that satisfies the IQCs. Furthermore, we connect our new definition
of the spectral radius to the existing literature on IQCs.
