On the uniform input-to-state stability of reaction-diffusion systems

In the present paper we consider uniform input-to-state stability of reaction-diffusion equations and compare it with its finite dimensional counterpart without diffusion as a parameterized set of decoupled equations. The reaction-diffusion partial differential equation can be seen as their interconnection via diffusion. We prove, that for linear reaction-diffusion systems and certain classes of nonlinear equations the UISS property for corresponding systems without diffusion implies, that the UISS property holds also for the system with diffusion.