The paper uses a frequency domain method for the boundary control of hyperbolic conservation laws. We show that the transfer function of the hyperbolic system belongs to the Callier-Desoer algebra, which opens the way of sound results, and in particular to the existence of a necessary and sufficient condition for the closed loop stability and the use of Nyquist type test. We examine the link between input-output stability and exponential stability of the state. Specific results are then derived for the case of proportional diagonal boundary controllers. The results are illustrated in the case of diagonal boundary control of open channel flow. (C) 2008 Elsevier Ltd. All rights reserved.