A unified approach to structure and controller design optimization is examined. Difficult problems arise in a unified approach, namely, a high dimensioned design space, nonlinearity, complexity of constraints and many inequality constraints. As a candidate for overcoming the above problems, an optimization algorithm utilizing sequential linear programming and continuation methods is proposed. The second part of this dissertation examines various ideas associated with both theory and practical issues arising in optimizing for eigenvalue sensitivity and stability robustness with respect to parameter variations or unstructured uncertainties. In particular, the time domain approach to stability robustness is pursued. It is found that a recently proposed stability robustness criteria of Patel and Toda is related to well known concepts of numerical conditioning of the eigenvalue problem and may be derived concisely using eigenvalue conditioning concepts. In addition, we review the more direct and perhaps less rigorous approach of dealing with uncertainties, namely modal insensitivity theory. The mathematical conditions for achieving modal insensitivity and eigenvalue placement simultaneously are reviewed along with a discussion of the practical merit of these ideas. As an alternative, we derive a scalar measure of eigenvalue sensitivity which is a linearly predicted bound on weighted eigenvalue perturbation; we also introduce an algorithm for minimization of this index. Furthermore, the expressions for eigenvector derivatives are correctly derived for non-self-adjoint case. This latter contribution corrects errors present in at least two textbooks on the subject and serves to clear up confusion in the literature. Finally, we use examples to demonstrate the design algorithm proposed here and numerically examine various designs arising from corresponding cost functions, using a specific configuration (a flexible free-free beam with an attached rigid body.) The numerical results confirm the conservatism of the stability robustness bound for highly structured perturbations but nevertheless clearly supports the hypothesis that maximizing the robustness measure significantly increases the true robustness of a closed loop system. The numerical results also indicate that maximizing the stability robustness measure is better (more efficient computationally and produces more robust designs) than minimizing the eigenvalue sensitivities directly for improving true stability robustness with respect to perturbations in the closed loop system matrix. / Ph. D. / incomplete_metadata