A conformal mapping approach to a root-clustering problem

European Workshop on Advanced Control and Diagnosis

Melnikov, Gennady I.^1 ; Dudarenko, Nataly A.^2 ; Melnikov, Vitaly G.^1

Department of Theoretical and Applied Mechanics, University ITMO, St.Petersburg, Russia^1

Department of Management Systems and Informatics, University ITMO, St.Petersburg, Russia^2

关键词: Cassini;    Clustering problems;    Complex planes;    Forbidden region;    Matrix root-clustering;    Multiply connected regions;    New approaches;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/570/2/022004/pdf
DOI  :  10.1088/1742-6596/570/2/022004

来源: IOP

【 摘 要 】

This paper presents a new approach for matrix root-clustering in sophisticated and multiply-connected regions of the complex plane. The parametric sweeping method and a concept of the closed forbidden region covered by a set of modified three-parametrical Cassini regions are used. A conformal mapping approach was applied to formulate the main results of the paper. An application of the developed method to the problem of matrix root-clustering in a multiply connected region is shown for illustration.