Robust Control Design of Underactuated 2 × 2 PDE-ODE-PDE Systems

In this letter, we design a robust stabilizing controller for system composed of two sets linear heterodirectional hyperbolic PDEs, with actuation at one boundary the and couplings middle ODEs in PDE-ODE-PDE configuration. The is underactuated since only PDE systems actuated. approach employs backstepping transformation to move undesired proximal (where located). We can then express target as time-delay neutral which an appropriate control law obtain exponentially stable system.