Zero and pole dynamics for a controlled Burgers´ equation

Our primary goal is to report on the results obtained in the author´s recent work (1994) for a closed loop boundary controlled Burgers´ system with dynamics in the state space of square integrable functions on a finite interval. For small initial data and disturbances in L², we have shown that as the closed loop system gains lend to infinity, the trajectories of the closed loop system converge in L² to the trajectories of the zero dynamics, i.e., the systems obtained by constraining the system output to zero. For slightly stronger assumptions on the external forcing term (disturbance) it can be shown that the trajectories converge in H¹(0,1) and hence uniformly