Performance limitations in reference tracking and path following for nonlinear systems

We investigate limits of performance in reference tracking and path following and highlight an essential difference between them. For a class of nonlinear systems, we show that in reference tracking, the smallest achievable L2L2 norm of the tracking error is equal to the least amount of control energy needed to stabilize the zero dynamics of the error system. We then show that this fundamental performance limitation does not exist when the control objective is to force the output to follow a geometric path without a timing law assigned to it. This is true even when an additional desired speed assignment is required to be satisfied asymptotically or in finite time.