An optimal differential sensitivity approach to pole assignment for structurally perturbed systems

This paper introduces a mathematical formula for calculating the eigenvalue differential sensitivities of the closed-loop state matrix with respect to a disturbance matrix when the closed-loop system is subjected to an additi ve structured perturbation. The robust pale assignment problem is then form ulated as an optimization task in which the differential sensitivities of t he closed-loop poles are minimized. The case of "multi-perturbations" can b e considered naturally in our problem formulation. The gradient of the obje ctive function to be minimized is then derived which permits the minimizati on to be proceeded effectively. Numerical examples are then employed to ill ustrate the design technique.