Rates of change of closed‐loop eigenvalues and eigenvectors of actively controlled structures

The sensitivity of the closed-loop eigenvalues and eigenvectors of actively controlled flexible structures with distinct eigenvalues is considered. The sensitivity information is essential in the optimization of large space structures with stability/performance robustness, closed-loop eigenvalues or damping ratios treated as objective or constraint functions. The efficiency of the analytical expressions derived for the rates of change of the closed-loop eigenvalues with respect to structural design variables is demonstrated through two numerical examples. The utility of the sensitivity of the closed-loop eigenvalues and eigenvectors in evaluating the derivatives of the stability and performance robustness indices is also indicated and illustrated through numerical examples.