The S-procedure

Abstract

In this chapter, we present a collection of results concerning the so called S-procedure. The term “S-procedure” was introduced by Aizerman and Gantmacher in the monograph [2] (see also [65]) to denote a method which had been frequently used in the area of nonlinear control; e.g., see [119, 112, 169]. More recently, similar results have been extensively used in the Western control theory literature and the name S-procedure has remained; e.g., see [127, 185, 190, 210, 26]. As mentioned in Section 1.2, a feature of the S-procedure approach is that it allows for non-conservative results to be obtained for control problems involving structured uncertainty. In fact, the S-procedure provides a method for converting robust control problems involving structured uncertainty into parameter dependent problems involving unstructured uncertainty. Furthermore, S-procedure methods find application to many robust control problems not included in this book; e.g., see [196, 131, 202]. A general and systematic description of the S-procedure can be found, for example, in the monograph [67].