### Abstract

The intention of the paper is to demonstrate the beauty of geometric interpretations in robust control. We emphasize Klein's approach, i.e., the view in which geometry should be defined as the study of transformations and of the objects that transformations leave unchanged, or invariant. We demonstrate through the examples of the basic control tasks that a natural framework to formulate different control problems is the world that contains as points the equivalence classes determined by the stabilizable plants and whose natural motions are the Möbius transforms. Transformations of certain hyperbolic spaces put light into the relations of the different approaches, provide a common background of robust control design techniques and suggest a unified strategy for problem solutions. Besides the educative value a merit of the presentation for control engineers might be a unified view on the robust control problems that reveals the main structure of the problem at hand and give a skeleton for the algorithmic development.

Original language | English |
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Title of host publication | 19th IFAC World Congress IFAC 2014, Proceedings |

Publisher | IFAC Secretariat |

Pages | 718-723 |

Number of pages | 6 |

Volume | 19 |

ISBN (Print) | 9783902823625 |

Publication status | Published - 2014 |

Event | 19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014 - Cape Town, South Africa Duration: Aug 24 2014 → Aug 29 2014 |

### Other

Other | 19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014 |
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Country | South Africa |

City | Cape Town |

Period | 8/24/14 → 8/29/14 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*19th IFAC World Congress IFAC 2014, Proceedings*(Vol. 19, pp. 718-723). IFAC Secretariat.

**A hyperbolic view on robust control.** / Szabó, Z.; Bokor, J.; Vamos, T.

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

*19th IFAC World Congress IFAC 2014, Proceedings.*vol. 19, IFAC Secretariat, pp. 718-723, 19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014, Cape Town, South Africa, 8/24/14.

}

TY - GEN

T1 - A hyperbolic view on robust control

AU - Szabó, Z.

AU - Bokor, J.

AU - Vamos, T.

PY - 2014

Y1 - 2014

N2 - The intention of the paper is to demonstrate the beauty of geometric interpretations in robust control. We emphasize Klein's approach, i.e., the view in which geometry should be defined as the study of transformations and of the objects that transformations leave unchanged, or invariant. We demonstrate through the examples of the basic control tasks that a natural framework to formulate different control problems is the world that contains as points the equivalence classes determined by the stabilizable plants and whose natural motions are the Möbius transforms. Transformations of certain hyperbolic spaces put light into the relations of the different approaches, provide a common background of robust control design techniques and suggest a unified strategy for problem solutions. Besides the educative value a merit of the presentation for control engineers might be a unified view on the robust control problems that reveals the main structure of the problem at hand and give a skeleton for the algorithmic development.

AB - The intention of the paper is to demonstrate the beauty of geometric interpretations in robust control. We emphasize Klein's approach, i.e., the view in which geometry should be defined as the study of transformations and of the objects that transformations leave unchanged, or invariant. We demonstrate through the examples of the basic control tasks that a natural framework to formulate different control problems is the world that contains as points the equivalence classes determined by the stabilizable plants and whose natural motions are the Möbius transforms. Transformations of certain hyperbolic spaces put light into the relations of the different approaches, provide a common background of robust control design techniques and suggest a unified strategy for problem solutions. Besides the educative value a merit of the presentation for control engineers might be a unified view on the robust control problems that reveals the main structure of the problem at hand and give a skeleton for the algorithmic development.

UR - http://www.scopus.com/inward/record.url?scp=84929719859&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929719859&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783902823625

VL - 19

SP - 718

EP - 723

BT - 19th IFAC World Congress IFAC 2014, Proceedings

PB - IFAC Secretariat

ER -