Stabilization of a hyperbolic PDEs-ODE network using a recursive dynamics interconnection framework

In this paper, we design a state-feedback law that exponentially stabilizes an underactuated network of scalar hyperbolic systems coupled at the end of the chain with a finite-dimensional system modeled by an ordinary differential equation. Our approach uses a recursive dynamics interconnection framework. More precisely, for each subsystem, we solve a stabilization problem, a tracking problem and design a state-predictor. Then, we are able to recursively design a control law that stabilizes the whole chain. Some illustrative examples complete the presentation.