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The S-procedure

  • Ian R. Petersen
  • Valery A. Ugrinovskii
  • Andrey V. Savkin
Chapter
  • 662 Downloads
Part of the Communications and Control Engineering book series (CCE)

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].

Keywords

Quadratic Form Convex Cone Continuous Curve Quadratic Constraint Structure Uncertainty 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2000

Authors and Affiliations

  • Ian R. Petersen
    • 1
  • Valery A. Ugrinovskii
    • 1
  • Andrey V. Savkin
    • 2
  1. 1.School of Electrical EngineeringADFACanberraAustralia
  2. 2.Department of Electrical and Electronic EngineeringUniversity of Western AustraliaNedlandsAustralia

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