This paper is concerned with the study of bidirectionally coupled platoon systems. The case considered is when the vehicles are heterogeneous and the coupling can be nonlinear and asymmetric. For such systems, a sufficient condition for L-infinity string stability is presented. The effectiveness of our approach is illustrated via a numerical example, where it is shown how our result can be recast as an optimization problem, allowing to design the control protocol for each vehicle independently on the other vehicles and hence leading to a bottom-up approach for the design of string stable systems able to track a time-varying reference speed. (C) 2019 Elsevier Ltd. All rights reserved.