Robust tracking for a class of uncertain linear systems

Tracking of a specified nominal output within an arbitrary error bound in the presence of uncertainties is formulated in terms of topological neighbourhoods in the function space Lκ∞ [0, ∞). It is shown that an observer-based state-feedback controller can be constructed to effect the desired robust tracking for a class of multi-input-multi-output linear systems containing uncertain parameters. The controller and the observer gains for this structure are chosen on the basis of a quantitative pole placement. This pole placement is based on an inequality arrived at by separating the uncertain effects of the true system from a nominal set of equations containing no uncertainties. The applicability of the proposed scheme is illustrated by synthesizing a controller for a second-order system.