Title :
Explicit SOS decompositions of univariate polynomial matrices and the Kalman-Yakubovich-Popov lemma
Author :
Aylward, Erin M. ; Itani, Sleiman M. ; Parrilo, Pablo A.
Author_Institution :
BBN Technol., Cambridge
Abstract :
The purpose of this paper is twofold. The first is to make explicit the relationship between sum of squares (SOS) decompositions of univariate polynomial matrices and the Kalman-Yakubovich-Popov (KYP) lemma. The second is to present an efficient algorithm for explicitly finding an SOS decomposition of such matrices, inspired by the Hamiltonian-type methods for the solution of Riccati equations.
Keywords :
matrix decomposition; polynomial matrices; Hamiltonian-type methods; Kalman-Yakubovich-Popov lemma; Riccati equations; sum of squares decompositions; univariate polynomial matrices; Control systems; Linear matrix inequalities; Matrix decomposition; Optimization methods; Polynomials; Riccati equations; Signal processing; Signal processing algorithms; Terminology; USA Councils;
Conference_Titel :
Decision and Control, 2007 46th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
978-1-4244-1497-0
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2007.4435026
