  We propose an optimization approach to the solution of the partial quadratic
eigenvalue assignment problem (PQEVAP) for active vibration control design with
robustness (RPQEVAP). The proposed cost function is based on the concept of
sensitivities over the sum and the product of the closed-loop eigenvalues,
introduced recently in our paper. Explicit gradient formula for the solutions
using state feedback and derivative feedback are derived as functions of a free
parameter. These formulas are then used to build algorithms to solve RPQEVAP in
a numerically efficient way, with no need to compute new eigenvectors, for both
state feedback and state-derivative feedback designs. Numerical experiments are
carried out in order to demonstrate the effectiveness of the algorithms and to
compare the proposed method with other methods in the literature, thus showing
its effectiveness.
