H∞Model Match Output-Feedback Control by Means of an LMI-Based Algorithm

Abstract

This letter addresses the problem of model match control for uncertain continuous-time linear systems by means of fixed order dynamic output-feedback. The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm is used as performance metric for the approximation error and the synthesis conditions are formulated in terms of LMIs, which are solved iteratively. The novelty of the approach with respect to previous results is that the matrices of the controller, as well as the matrices of the reference model, appear affinely in the conditions, allowing the immediate treatment of structured controllers and providing extra degrees of freedom for the reference model, in the sense that some of the entries of the matrices do not need to be fixed a priori and, therefore, can be determined by the synthesis conditions. This latter feature allows an extension of the method to address the problem of order reduction of uncertain systems. The results are illustrated by an example based on a model borrowed from the literature.