We consider the stabilization problem for linear systems of balance laws subject to uncertain gains affecting the boundary conditions and the reaction term. The stabilization is achieved using the supervisory control, a well established approach in finite dimension. In the context where a controller exists for each estimator, the supervisory control with a performance signal built with the boundary output effectively steers the system to the origin. This novel approach is illustrated with a traffic flow control problem modeled by the Aw-Rascle-Zhang equations. (C) 2019 Elsevier Ltd. All rights reserved.