Stability and the Kleinian view of geometry

Z. Szabó, József Bokor

Research output: Chapter in Book/Report/Conference proceedingChapter


Youla parametrization of stabilizing controllers is a fundamental result of control theory: starting from a special, double coprime, factorization of the plant provides a formula for the stabilizing controllers as a function of the elements of the set of stable systems. In this case the set of parameters is universal, i.e., does not depend on the plant but only the dimension of the signal spaces. Based on the geometric techniques introduced in our previous work this paper provides an alternative, geometry based parametrization. In contrast to the Youla case, this parametrization is coordinate free: it is based only on the knowledge of the plant and a single stabilizing controller. While the parameter set itself is not universal, its elements can be generated by a universal algorithm. Moreover, it is shown that on the parameters of the strongly stabilizing controllers a simple group structure can be defined. Besides its theoretical and educative value the presentation also provides a possible tool for the algorithmic development.

Original languageEnglish
Title of host publicationLecture Notes in Control and Information Sciences
PublisherSpringer Verlag
Number of pages34
Publication statusPublished - Jan 1 2020

Publication series

NameLecture Notes in Control and Information Sciences
ISSN (Print)0170-8643

ASJC Scopus subject areas

  • Library and Information Sciences

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    Szabó, Z., & Bokor, J. (2020). Stability and the Kleinian view of geometry. In Lecture Notes in Control and Information Sciences (pp. 57-90). (Lecture Notes in Control and Information Sciences; Vol. 482). Springer Verlag.