  We study the stability margin of a vehicular formation with distributed
control, in which the control at each vehicle only depends on the information
from its neighbors in an information graph. We consider a D-dimensional lattice
as information graph, of which the 1-D platoon is a special case. The stability
margin is measured by the real part of the least stable eigenvalue of the
closed-loop state matrix, which quantifies the rate of decay of initial errors.
In [1], it was shown that with symmetric control, in which two neighbors put
equal weight on information received from each other, the stability margin of a
1-D vehicular platoon decays to 0 as O(1/N^2), where N is the number of
vehicles. Moreover, a perturbation analysis was used to show that with
vanishingly small amount of asymmetry in the control gains, the stability
margin scaling can be improved to O(1/N). In this paper, we show that, with
judicious choice of non-vanishing asymmetry in control, the stability margin of
the closed loop can be bounded away from zero uniformly in N. Asymmetry in
control gains thus makes the control architecture highly scalable. The results
are also generalized to D-dimensional lattice information graphs that were
studied in [2], and the correspondingly stronger conclusions than those derived
in [2] are obtained. In addition, we show that the size-independent stability
margin can be achieved with relative position and relative velocity (RPRV)
feedback as well as relative position and absolute velocity (RPAV) feedback,
while the analysis in [1], [2] was only for the RPAV case.
