Boundary control of hyperbolic conservation laws using a frequency domain approach

The paper uses a frequency domain method for boundary control of hyperbolic conservation laws. We show that the transfer function of the hyperbolic system belongs to the Callier-Desoer algebra, for which the Nyquist theorem provides necessary and sufficient conditions for input-output closed-loop stability. We examine the link between input-output stability and exponential stability of the state. Specific results are then derived for the case of proportional boundary controllers. The results are illustrated in the case of boundary control of open-channel flow