An important aspect of an Automated Highway System is automatic vehicle following. Automatic Vehicle follower systems must address the problem of string stability, i.e., the problem of spacing error propagation, and in some cases, amplification upstream from one vehicle to another, due to some disturbance at the head of the platoon. An automatic vehicle following controller design that is (asymptotically) stable for one vehicle following another is not necessarily (asymptotically) stable for a string of vehicles. The dynamic coupling between vehicles in such close-formation platoons is a function of the available information (communicated as well as sensed), decentralized feedback control laws and the vehicle spacing policy in use. In the first half of this paper, we develop a framework for establishing conditions for stability of the string in the presence of such dynamic interactions. We then develop a metric for analyzing the performance of a platoon resulting from different vehicle following control algorithms. This metric is the guaranteed rate of attenuation/non-amplification of spacing errors from one vehicle to another. In the latter half of this paper, we outline and analyze various constant spacing vehicle follower algorithms. All these algorithms are analyzed for sensing/actuation lags.