Robust stability of a nonlinear ode-pde system

This work studies stability and robustness of a nonlinear system given as an inter-connection of an ODE and a parabolic PDE subjected to external disturbances entering through the boundary conditions of the parabolic equation. To this end we develop an approach for construction of a suitable coercive Lyapunov function as one of our main results. Based on this Lyapunov func-tion, we establish well-posedness of the considered system and establish conditions that guarantee the input-to-state stable (ISS) property. ISS estimates are derived explicitly for the particular case of globally Lipschitz nonlinearities.