Stabilization of coupled linear heterodirectional hyperbolic PDE-ODE systems

We solve the problem of stabilizing a linear ODE having a system of a linearly coupled hyperbolic PDEs in the actuating path. The control design is based on a backstepping approach and yields exponential closed-loop stability of the zero equilibrium. The existence of a Volterra transformation relies on a relatively general well-posedness result for hyperbolic backstepping kernel equations.