Path-following for Linear Systems with Unstable Zero Dynamics

Authors:	Dacic Dragan B., University of California, Santa Barbara, United States Kokotovic Petar V., University of California, Santa Barbara, United States
Topic:	2.2 Linear Control Systems
Session:	Analysis and Synthesis of Linear Control Systems I
Keywords:	Reference tracking, path-following, unstable zero dynamics, performance limitations

Abstract

A path-following problem for linear systems with unstable zerodynamics is solved. While the original control variable steers thesystem output along the path, the path parameter $\theta$ is usedas an additional control to stabilize zero dynamics with afeedback law which is nonlinear due to the path constraint. Asufficient condition for solvability of the path-following problemis given in terms of the geometric properties of the path. Whenthis condition is satisfied, an arbitrary small $\mathcal{L}_2$ norm ofpath-following error can be achieved.