In this dissertation, a new approach to perturbations of state feedback H$\sb{\infty}$ optimization techniques has been developed. New methods based on sensitivity theory have been devised that make application of formal H$\sb{\infty}$ synthesis techniques to feedback system design more efficient. The sensitivity of the state feedback H$\sb{\infty}$ synthesis optimal solution is quantified for a certain class of regular and singular perturbations. This dissertation considers the problem of adjusting H$\sb{\infty}$ weighting functions to improve design by parametric variations. Estimates for open and closed loop transfer functions are provided to assess the parametric change in design. Full state is assumed to be available for feedback in this dissertation. Both regular perturbation and singular perturbation results have been developed for high frequency variations in weighting functions. The state feedback H$\sb{\infty}$ optimal solution is characterized in order to estimate the first order change in the H$\sb{\infty}$ optimal value as a result of both regularly and singularly perturbed weighting functions used as design parameters.

Large chemical plants are usually designed by combining several individually well controlled process units into a whole. This practice produces satisfactory, controlled response if the dynamic interactions are "weak". However, high material and energy costs and increased market competition have driven chemical plants towards a higher degree of energy integration and material recycle. These "modern" plants become difficult to operate and control because strong interconnections generally degrade the performance of the individual units, and in some cases the total response for the plant may be unstable. Our study focuses on modifying the plant design and improving control configurations to regain stability and to obtain the original output trajectories of the units as closely as possible. Via a sequential procedure, we represent the plant by a hierarchical set of self-similar modules, in which the top level represents the entire plant. The analysis of the synthesis procedures depends on a proposed measure of interaction, $\phi$, whose minimization produces the required guidelines for stable design and control.