3. Feedback stabilization

As we have already seen, hyperbolic partial differential equations of the balance equation type can be used to model many physical systems, such as fluid motion (Saint-Venant equations) or drilling systems. In the previous section, we proposed methods for analyzing the behavior of such systems, and in particular their stability properties. When considering an industrial application, it is generally desirable for system variables to "behave well" and follow a pre-defined reference value. In most configurations, however, the natural dynamics of the system cannot guarantee such behavior. It is therefore necessary to act on the system via one or more actuators, and to find the control law that will guarantee the system's correct behavior. In particular, we aim to stabilize the system around this reference variable, and thus to stabilize the deviation between system variables and their reference...