Robust eigenstructure assignment with minimum subspace separation

Abstract

A computation method for delivering a state feedback controller that assigns closed-loop eigenstructure with a minimum subspace separation and is robust towards unstructured perturbations is presented. The subspace separation is measured via the difference between two subspace projections, while the eigenstructure robustness is achieved by maximizing an upper bound on the allowable perturbation size such that the closed-loop system remains stable. By exploiting the Sylvester equation parametrization, the constraint of pole assignment can be satisfied intrinsically and the robust eigenstructure assignment design essentially becomes an unconstrained optimization task. Analytical gradient formulas of the objective functions to be handled are developed. The design approach is demonstrated through numerical examples. Copyright © 2004 John Wiley & Sons, Ltd.