  In this paper, we give necessary conditions for stability of coupled
autonomous vehicles in R. We focus on linear arrays with decentralized
vehicles, where each vehicle interacts with only a few of its neighbors. We
obtain explicit expressions for necessary conditions for stability in the cases
that a system consists of a periodic arrangement of two or three different
types of vehicles, i.e. configurations as follows: ...2-1-2-1 or
...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition
for stability in the case of a single vehicle type (...1-1-1) held that the
first moment of certain coefficients of the interactions between vehicles has
to be zero. Here, we show that that does not generalize. Instead, the
(necessary) condition in the cases considered is that the first moment plus a
nonlinear correction term must be zero.
