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 0 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 L-2 norm of path-following error can be achieved, thus avoiding performance limitations of the standard reference tracking problem imposed by unstable zero dynamics. (C) 2006 Elsevier Ltd. All rights reserved.