On the Synthesis of Fixed Structure Controllers Satisfying given Performance Criteria

Abstract

Many practical applications require the design of fixed order and structure feedback controllers. It is often required that these feedback controllers satisfy some specified criterion. This class of fixed structure controller synthesis problems can be reduced to the determination of a real controller parameter vector (or simply a controller), K, so that a family of complex polynomials, linear in the parameters of the controllers, is Hurwitz. A novel feature of this paper is the exploitation of the Interlacing Property (IP) of complex Hurwitz polynomials to systematically generate an arbitrarily large number of sets of linear inequalities in K. The simultaneous stabilization of the family of complex polynomials provides an approximation of the required set of controllers. We provide examples of the applicability of the proposed methodology to the synthesis and design of fixed order controllers.