On the positivity of polynomials on the complex unit disc via LMIs

Author

Chesi, Graziano

Author_Institution

Dept. of Electr. & Electron. Eng., Univ. of Hong Kong, Hong Kong, China

fYear

2012

fDate

April 29 2012-May 2 2012

Firstpage

1

Lastpage

4

Abstract

Investigating positivity of polynomials over the complex unit disc is a relevant problem in electrical and computer engineering. This paper provides two sufficient and necessary conditions for solving this problem via linear matrix inequalities (LMIs). These conditions are obtained by exploiting trigonometric transformations, a key tool for the representation of polynomials, and results from the theory of positive polynomials. Some numerical examples illustrate the proposed conditions.

Keywords

computational geometry; linear matrix inequalities; polynomials; LMI; complex unit disc; computer engineering; electrical engineering; linear matrix inequalities; polynomial positivity; polynomial representation; trigonometric transformations; Convex functions; Eigenvalues and eigenfunctions; Linear matrix inequalities; Optimization; Polynomials; Symmetric matrices; Transfer functions; Discrete time; LMI; Linear system; Positivity; Transfer function;

fLanguage

English

Publisher

ieee

Conference_Titel

Electrical & Computer Engineering (CCECE), 2012 25th IEEE Canadian Conference on

Conference_Location

Montreal, QC

ISSN

0840-7789

Print_ISBN

978-1-4673-1431-2

Electronic_ISBN

0840-7789

Type

conf

DOI

10.1109/CCECE.2012.6334819

Filename

6334819