Path-following for linear systems with unstable zero dynamics

A constructive solution to the path-following problem for MIMO linear systems with unstable zero dynamics is developed. While the original control variable steers the system output along the path, the path parameter θθ is used as an additional control to stabilize zero dynamics with a feedback law which is nonlinear due to the path constraint. A sufficient condition for solvability of the path-following problem is given in terms of the geometric properties of the path. When this condition is satisfied, an arbitrary small L2L2 norm of path-following error can be achieved, thus avoiding performance limitations of the standard reference tracking problem imposed by unstable zero dynamics.