We consider in this paper three different partial differential equations (PDEs) that can be exponentially stabilized using
backstepping controllers. For implementation, a finite-dimensional controller is generally needed. The backstepping controllers
are approximated and it is proven that the finite-dimensional approximated controller stabilizes the original system if the order
is high enough. This approach is known as late-lumping. The other approach to controller design for PDE’s first approximates
the PDE and then a controller is designed; this is known as early lumping. Simulation results comparing the performance of
late-lumping and early-lumping controllers are provided.