Sum-of-Squares Decomposition via Generalized KYP Lemma

Author

Hara, S. ; Iwasaki, T.

Author_Institution

Dept. of Inf. Phys. & Comput., Univ. of Tokyo, Tokyo

Volume

54

Issue

5

fYear

2009

fDate

5/1/2009 12:00:00 AM

Firstpage

1025

Lastpage

1029

Abstract

The Kalman-Yakubovich-Popov (KYP) lemma establishes the equivalence between a frequency domain inequality (FDI) of a proper rational function and a linear matrix inequality (LMI). A recent result generalized the KYP lemma to characterize an FDI of a possibly nonproper rational function on a portion of a curve on the complex plane. This note examines implications of the generalized KYP result to sum-of-squares (SOS) decompositions of matrix-valued nonnegative polynomials of a single complex variable on a curve in the complex plane. Our result generalizes and unifies some existing SOS results, and also establishes equivalences among FDI, LMI, and SOS.

Keywords

linear matrix inequalities; polynomials; rational functions; Kalman-Yakubovich-Popov lemma; frequency domain inequality; linear matrix inequality; matrix-valued nonnegative polynomials; rational function; sum-of-squares decomposition; Digital control; Digital filters; Fault detection; Frequency domain analysis; Linear matrix inequalities; Linear programming; Matrix decomposition; Polynomials; Robust control; Transfer functions; Generalized Kalman–Yakubovich–Popov (KYP) lemma; positive polynomials; sum-of-squares decomposition;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2009.2017149

Filename

4908928