Delay robust control design of under-actuated PDE-ODE-PDE systems

We propose a controller design for a system composed of two sets of linear heterodirectional hyperbolic PDEs, with actuation at one boundary, and coupled at the other boundary by ODEs in a PDE-ODE-PDE configuration. The design approach employs a backstepping transformation, however, the under-actuation limits the choice of target system. To deal with this limitation, we propose to use stability results from delay systems to find a stable target system. Furthermore, we propose to use a high-pass filter of the proximal reflection, in place of cancellation, to obtain controllers that are robust to small delays.