Robust pole-placement for ellipsoidally uncertain systems

A technique is proposed for synthesizing pole-placement controllers capable of assigning the closed-loop poles of an family of plants inside a specified design region. The design is applicable to plants characterized by uncertain parameters that are known to lie inside an ellipsoid. Ellipsoidal parametric uncertainty descriptions are particularly useful because they arise naturally in the context of parameter estimation, and hence have the advantage of being quantifiable using experimental input-output data. The control-design problem is posed as a minimax program that is shown to be convex, and that can be solved using numerical techniques with global convergence guarantees.