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# Perturbations of H-infinity state feedback systems

#### Abstract

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.

#### Subject Area

Systems design|Electrical engineering

#### Recommended Citation

Geray, Okan, "Perturbations of H-infinity state feedback systems" (1996). Doctoral Dissertations Available from Proquest. AAI9709599.
https://scholarworks.umass.edu/dissertations/AAI9709599

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