On the structure and implementation of the optimal Q-Parameter in the one-block H-infinity control problem

Abstract

In the robust control theory, H∞ methods are carried out to procure solutions to sensitivity minimization (nominal performance) and robust stability problems in general. These one – block control problems can be analyzed separately or in a combined fashion. In the general sense, the design of the robust controller is made to achieve stability and performance objectives for a plant, whose nominal model and uncertainty bounds can be determined from the experimental data. This study aims to present a solution to infinite dimensional one – block H∞ control problem and provide a general structural result for Q – Parameter. The methods like Nevanlinna – Pick interpolation will not work for infinite dimensional control problems whereas Sarason’s Theorem provides solution to infinite dimensional control problems. In this thesis, Sarason’s Theorem is analyzed and examined extensively and applied on infinite dimensional one – block H∞ control problem. The detailed structural analysis of the resulting Q – Parameter is made as the main contribution of the thesis. Various examples are given to illustrate the computational issues. In this analysis, stability status of Q – Parameter is demonstrated by examining stable terms and FIR part of its sub – blocks.