### Abstract

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 language | English |
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Title of host publication | Lecture Notes in Control and Information Sciences |

Publisher | Springer Verlag |

Pages | 57-90 |

Number of pages | 34 |

DOIs | |

Publication status | Published - Jan 1 2020 |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Volume | 482 |

ISSN (Print) | 0170-8643 |

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### ASJC Scopus subject areas

- Library and Information Sciences

### Cite this

*Lecture Notes in Control and Information Sciences*(pp. 57-90). (Lecture Notes in Control and Information Sciences; Vol. 482). Springer Verlag. https://doi.org/10.1007/978-3-030-18572-5_2

**Stability and the Kleinian view of geometry.** / Szabó, Z.; Bokor, József.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Lecture Notes in Control and Information Sciences.*Lecture Notes in Control and Information Sciences, vol. 482, Springer Verlag, pp. 57-90. https://doi.org/10.1007/978-3-030-18572-5_2

}

TY - CHAP

T1 - Stability and the Kleinian view of geometry

AU - Szabó, Z.

AU - Bokor, József

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=85068139654&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-18572-5_2

DO - 10.1007/978-3-030-18572-5_2

M3 - Chapter

AN - SCOPUS:85068139654

T3 - Lecture Notes in Control and Information Sciences

SP - 57

EP - 90

BT - Lecture Notes in Control and Information Sciences

PB - Springer Verlag

ER -