Time delay and wave propagation in controlling systems of conservation laws

In this paper there are considered some applications arising from power engineering and involving hyperbolic equations of conservation laws. Focusing on the control of the flow in open channels, there is considered the linearized model and a Lyapunov functional is associated. A linear multivariable controller with saturation is synthesized to make the Lyapunov functional exponentially decreasing along the solutions of the closed loop system. By integrating the Riemann invariants along the characteristics there is associated a linear system of difference equations. On this system the basic theory is constructed and the stability verified. Finally a research program for analyzing nonlinear cases is sketched.