Backstepping stabilization of an underactuated 3 × 3 linear hyperbolic system of fluid flow equations

We investigate the boundary stabilization of a particular subset of 3×3 linear hyperbolic systems with varying coefficients on a bounded domain. The system is underactuated since only one of the three hyperbolic PDEs is actuated at the boundary. The setup considered in the paper occurs in control of multiphase flows on oil production systems. We use a backstepping approach to design a full-state feedback law yielding exponential stability of the origin.