A Mobius Transformation for Algebraic Dynamical Systems

Author

Tudor, Sebastian F. ; Oara, Cristian

Author_Institution

Dept. of Autom. Control & Syst. Eng., ”Politeh.” Univ. of Bucharest, Bucharest, Romania

fYear

2015

fDate

27-29 May 2015

Firstpage

931

Lastpage

937

Abstract

A particular Mobius transformation mapping a completely general discrete-time algebraic dynamical system into a standard (proper) continuous-time one is introduced and studied. The freedom in choosing ab ante the exclusion point (in which the transformation is not defined) different from any point of interest makes this transformation a powerful universal tool for solving virtually any optimal/robust control problem for this class of systems by an elegant, yet simple reduction to known results. We show the effectiveness of our approach on two keystone problems: the normalized co prime factorization and the parametrization of all stabilizing controllers.

Keywords

algebra; continuous time systems; discrete time systems; linear systems; optimal control; robust control; transfer functions; LTI system; Mobius transformation mapping; discrete-time algebraic dynamical system; exclusion point; linear time-invariant system; normalized coprime factorization; optimal control problem; robust control problem; stabilizing controller parametrization; standard continuous-time system; transfer function; Biological system modeling; Control systems; Eigenvalues and eigenfunctions; Linear systems; Mathematical model; Polynomials; Standards;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Systems and Computer Science (CSCS), 2015 20th International Conference on

Conference_Location

Bucharest

Print_ISBN

978-1-4799-1779-2

Type

conf

DOI

10.1109/CSCS.2015.141

Filename

7168537