Guaranteed cost inequalities for robust stability and performance analysis

Abstract

In this paper, we formulate robust stability and performance bounds in terms of guaranteed cost inequalities. We derive new guaranteed cost bounds for plants with real structured uncertainty, and we reformulate them as linear matrix inequalities (LMIs). In particular, we obtain a shifted linear bound and a shifted inverse bound, and give LMI forms for a shifted bounded real bound, a shifted Popov bound, a shifted linear bound and a shifted inverse bound. Several examples are used to compare the shifted bounds with their unshifted counterparts and to make comparisons among these new bounds and vertex LMI bounds. Copyright © 2002 John Wiley & Sons, Ltd.