Robust eigenvalue assignment in second-order systems: A gradient flow approach

In this paper the problem of robust eigenvalue assignment in second-order systems by combined derivative and proportional state feedback is examined. It is shown that almost arbitrary assignment can be achieved by solving a linear matrix equation of symmetric linear system. Based on the fact that the robustness of the spectrum is characterized by the condition number of the eigenvectors, an alternative objective function is defined and minimized by utilizing the gradient flow technique. Numerical tests are performed to illustrate the approach.